Nope, not directly. But there are options:
You will need some 3rd party services that creates a kind of virtual network within the internet for the PCs you want to connect to..
LogMein works great and it is free :
https://secure.logmein.com/US/home.aspx
Basically all your pcs log into a central service [provided by LogmeIn] and then they can all interconnect . LogMeIn also got a free VPN one (call Hamachi) if you're not interested in Remote Desktop, but rather want to share files/FTP/devices between your PCs.
I believe someone explained it nicely a bunch of pages earlier in this thread. Basically all services that checks your IP will see -everyone- using Screamer as the one and same person. So it will look like one person is connecting from 3000 different PCs. Most services don't necissarily use your IP for anything and rather use your login/pw (that is why you create accounts) , but i.e. Rapidshare/Megaupload and such limits the amount of connections from the same IP. You will get messages like "you are already downloading something, please try later".
Obviously you won't be able to directly connect to your PC that are on Screamer from say your Work PC either (as mentioned above) because you don't have a unique IP. But fortunately there are ways around that with VPN technologies. But if you were thinking of hosting a website (or anything really) from your PC to the entire world, you might have a problem.....since you can't put the entire world on your little VPN .