I have p202 loaded on one server already.
Can I then just use it to track pages I have on other servers?
Yes. In the time it took you to write the post you could have tested it!! 
LOL!
But This way I get any reasons that might tell me this is the worst idea ever!
Actually it's a rather good idea. This way, if your Prosper server slows down for some reason, your landers don't slow down too - and vica versa, if some of your landers get snarled up for some reason, your Prosper doesn't end up biting the big one.