Negative, ghost rider. You cannot simply switch a hard drive to a different computer and expect they OS to run the same. However, and depending on whether or not you have an OEM or retail key, you can use software such as ProduKey to get your Windows key off of the old HDD, install a downloaded Windows 7 ISO onto a bootable drive, and then use the aforementioned key to activate Windows. This should work for you. The reason you cannot switch hard drives is because each system uses unique drivers specifically tailored to the hardware.
You can find the .iso here: http://www.w7forums.com/threads/official-windows-7-sp1-iso-image-downloads.12325/
and use an imaging software such as ImgBurn to put it on a USB. There are myriad forums dedicated to this, if you happen to run into trouble.