Been using Linux for 10 years and there is only one thing I can say to 'Will this work on…'
Wait until someone can say 'YES' to your specific problem, and is willing to walk you through the process.
Working under Linux doesn't always mean it will work for you, and certainly does not mean it will work under another architecture. Your best bet is to be patient and wait. There will be plenty of cheap offers once you have your Raspberry Pi and other more proficient Linux users can do all the work to find what does and doesn't go well with Pi (cream or custard?).
I will also take this opportunity to say, once you have the Pi running, then hard plugging it into a network and SSHing in with X-Deep/32 under Windows or your standard setup on a Linux box should be a doddle. This allows you to place the Pi next to the router and almost forget about it. No spare monitor or keyboard required (I'll post a howto on this later if no one else has and the demand exists).
Edit: Should also mention here, that the login is a full graphical one, not just a terminal.