That system only has Vista drivers it looks like, maybe XP. Some Vista drivers work with Win 7. If you want to try it, go for it. Since you will try it on a separate hard-drive you have nothing to lose. You can't damage the hardware if Win 7 does not work, and if it does not, gut put in your oringinal drive.
I have to say that based on many posts here and experience, if a laptop does not have drivers for an OS, I will have issues with at least some of the hardware. Usually Video and/or Audio.
This is a desktop. I heard of someone who said he did it, but it was a real pain in the butt. Acer will even tell you that they don't support 64 bit version of Vista on the E700 desktop. Generally, I find their support superficial and generally useless.