No,
In order to use a 3.5" Sata hard drive you must have a 12v supply to it.
The enclosure should of come with a 12v power supply.
Only a 2.5" laptop drive will work with a usb as they use 5+v and the Usb can provied 5v.
You need an external 12v to drive a 3.5" drive.
When you connect a 3.5" drive inside a tower or computer case the connection is 12v to it.
Now if you have 12v to the external drive and the usb connected.
You problem is a clash with letter assignments of windows.
In other words two drives share the same drive letter such as for example D: and D:
A internal and the external you connected.
So one will not show in the drive window of explorer.
You must if using windows 7, click on start.
In the search box type DISK MAN.
Click on the result that says format and create partitions.
A windows will open.
Click on actions, and re scan drives.
The usb drive will show up.
Now if the drive is new and just bought right click and format it.
If it has data on it you wish to keep.
Right click on the 1tb usb drive.
And select change drive letter or path.
Another box will open click on change.
On the right side select a drive letter not used by any other drive in the system or laptop eg H:
click ok.
Actions and re scan for drives. The same apply s for any partitions of each hard drive if there are any on both that clash or are duplicated.
The drive will then show up in windows my computer or explorer. or windows disk manager as for example as H: