Can we install Windows OS using USB drive (which has SSD controller - Corsair Flash Voyager® GTX ) ?

Yes, USBs can be boot devices.
http://lifehacker.com/5991848/how-to-boot-from-a-cd-or-usb-drive-on-any-pc
Enter the bios and choose boot device.
Choose you USB dive from the given choices.
Your computer should reboot and do what the USB tells it to.
As for installing programs onto USBs or making them local drives, I'm not too sure. I like video games and tried to install a small one on my flash drive and received a message saying that it will only install to local drives.

In that case it will have all the proprieties of a fixed drive and none of the limitations of a usb drive, so you shoud be able to do whatever you want with it, so long as teh BIOS sees it aswell.

Oops

I'm also interested in determining whether an OS can be booted from this Corsair model flash drive, particularly Win 10, however, my interest/scenario is somewhat different from yours.

My objective is to utilize the flash drive as a destination drive for the cloned contents of my Win 10 OS. While there's no problem with that objective using any flash drive having suitable capacity to contain the contents of the boot drive, I would like the flash drive to have bootable capability. Since the OS treats the usual flash drive as a removable device the resultant clone is not bootable.

However, as you point out, since this Corsair model uses a SSD controller I assume (more likely, hope!) the OS would treat the device as a Basic disk, and if so, the cloned Corsair would be bootable in the same way my cloned internally-connected and USB externally-connected drives are bootable.

Now if I correctly understand your situation you would desire to install the OS onto the USB-connected flash drive and you could directly boot to the OS. Do I have this right?

If so, our experience has been negative with regard to that situation. We have never been able to boot to an OS that was directly installed on (and connected as) a USB-connected device. This includes HDDs & SSDs that were connected as USB external drives. The attempt to install a Windows OS onto the drive always failed. However, strange as it seems, when an OS was CLONED to the USB-connected HDD or SSD the resultant clone was able to boot in most, but not all instances. Our disk-cloning program is Casper.

So...to summarize our experience in this area...
1. We are unable to fresh-install a Win OS onto a USB-connected drive.
2. We can effectively clone the contents of any OS bootable drive to a USB-connected HDD or SSD and in most cases the latter drive will be bootable as a USB-connected drive. BTW, we perform this operation for comprehensive backup purposes.

I would be most interested in learning about your experience with the Corsair flash drive re this issue.

There are ways to do that, but they are complicated. Just don;t bother and use a normal USb stick or a dvd to install.

Let me respond to your points 1. & 2. in which you responded to my summary of our experience using USB flash drives as a vehicle for the following capabilities...
1. Directly fresh-installing a Windows OS onto the USB-connected flash drive, and,
2. Using a flash drive as the recipient of the cloned contents of an internally-connected drive containing a Windows OS and utilizing that cloned flash drive as a bootable device.

As I trust I made clear, our experience has been with the usual type of USB flash drives available on the market, NOT the Corsair flash drive model that contains an SSD controller. I was particularly interested in the capability of this Corsair model as it relates to the OS installation experiences we've had with flash drives in general.

To reiterate...
1. We are all aware that we can utilize a USB flash drive to contain the Windows OS setup files downloaded from the appropriate Microsoft site. And we can use the flash drive containing those setup files as a vehicle to install a Windows OS onto an internally-connected HDD or SSD. There are no problems or issues in that area.

2. We CANNOT, however, directly fresh-install a Windows OS onto a USB-connected flash drive. This is ordinarily not permitted by a Microsoft OS. (The Windows To Go feature may be able to resolve this issue but since I've no experience with that feature I made no reference to it).

3. We CAN, however, clone the contents of a internally-connected drive containing an OS to a USB flash drive, however, the flash drive will not perform as a bootable device.

It is the potential capability expressed in 3. above that I'm especially interested in. I'm not particularly interested in whether an OS can be directly installed onto a USB flash drive (although I can appreciate it would be a nice feature for many users). So it is this capability that interests me and why I was thinking this Corsair model with its SSD controller would resolve this problem. And I'm hoping your personal experience (not theoretical manufacturer's specifications) with this Corsair would answer the question.

Well it won't be the quickest ever recorded install time possible. For that you would make a standard SSD the install media, to a second SSD as the destination. If even that is not fast enough for you, then you'd use PCIe x4 ore more lane SSDs as source and destination.

Frankly it is all a bit silly. Get a cheap small regular 16GB removable USB3 flash drive for OS install. You shouldn't need to be installing OS enough that the performance difference would matter, or if you admin a large group of PCs you'd be deploying partition images rather than individual OS installs. Deploying a partition image is much faster than installing Windows from scratch.

Plus, your idea about taking windows with you to run anywhere isn't go great because of the hardware differences regarding drivers, boot device ID, unique machine ID as it relates to OS validation, and more. I mean sure you could make it a portable OS instead, but you wrote "we can even use it at home" which makes little sense to do. If you care about performance, thus you are wanting this GTX model even if having to tackle it being a fixed drive, that performance is lower than using a tranditional SSD.

So you want a fast OS install, but a slower everyday use OS? It makes no sense.

Frankly, I'm somewhat baffled by your second paragraph.

It's a rather simple matter to create a Windows Media Tool containing the Win 10 setup files on a ordinary flash drive and then use that device to install the OS onto a fixed disk. We use an 8 GB or 16 GB flash drive to install the setup files but I believe even a slightly smaller capacity flash drive will be sufficient to contain the necessary files.
See... https://www.microsoft.com/en-us/software-download/windows10/

But surely you must be aware of this, no?

The installation process generally goes smoothly and reasonably quick. Since (hopefully) it's a one-shot process I don't see where speed of installation is an important consideration. What is important is that the installation results in a viable, fully-functional OS. All the rest is conversation as far as I'm concerned.

I have this Drive, GTX 256GB. I just used rufus to try install windows 7 ultimate from this respective drive. It does not work. The installation asks for a "driver" in order to be able to continue, but I have no such drivers and as such, I was not able to complete the installation.

Because this is not an ordinary USB flash drive, the windows installation needs a specific driver in order to handle and use this specific usb drive.