Depends, but I'm fairly sure the base station is logitech specific and won't talk to other mice.
I've had a logitech duo controller half-die on me before. The base station wouldn't talk to any mice, but the keyboard was fine and the mouse talked to a different logitech mouse base station. So it is possible to swap between some logitech mice, but they must be compatible.
Alternately, you can use two base stations, one for your mouse and one for your keyboard, assuming no interference issues (which is hard to know before you stick them next to each other and test).
If you're upgrading to a MX700 mouse (which is probably a safe bet, unless you want bluetooth), its controller isn't compatible with any others, but shouldn't interfere with anything else either. My current setup has a MX700 next to a non-bundled logitech keyboard (bought before they bundled the MX700 with any keyboard), and I don't have noticeable interference issues. If its not urgent, however, you might want to wait for the MX1000 though, which is rumored to be coming out "sometime soon".
And I just found this on the logitech website, which should answer your question a bit better:
http://logitech-en-amr.custhelp.com/cgi-bin/logitech_en_amr.cfg/php/enduser/std_adp.php?p_faqid=878