I actually did the same thing 2 weeks ago.It will work but it takes a very long time.I moved the Windows OS to the new drive and a few other applications.But some of the applications kinda freak out so you might have to reinstall them.Simple drag and drop.
So i could put the whole drive onto an external hard drive and once ive booted up my new computer with the new hard drive i can simply drag acrosss the say for instance " c " drive and the OS will come with it?
Actually no.I forgot that you cannot copy over the OS because windows is using it.You'll have to re-install windows on that HD but everything else you can copy over.Or what tecmo34 said use one of those programs so you don't have to reinstall.
With a 32 bits OS you maximum RAM will be slightly less than 4GB, probably in the range of 3.5-3.75GB depending if your video card uses part of the RAM.
Moreover, an OEM license is tied to the motherboard, not the HDD it was installed on so you can legally install it on another HDD on the same PC. However, I think many OEM ship them preactivated so I don't know how easily it can be reinstalled if you could get a hold of an installation DVD (license # should be on a sticker somewhere on the PC). A Windows 7 license is also valid for both 32 and 64 bits so switching should cause any licensing issue. I suggest you contact your PC's manufacturer and ask them how you should proceed to reinstall if you change the HDD; they might send you a "kit" for a few dollars (~20-30$).