The short answer: if its not running Windows Vista right now, probably not.
But here's a way to be sure; check out Microsoft's upgrade advisor.
Keep in mind the upgrade advisor is in beta, however this download will run a diagnostic on your system offering a print out of all the weak links requiring a tweek (unless it's beyond hope) to be Windows 7 ready.
Important note: make sure you have all your devices hooked up when you run the test. It can't give you the down-lo on your printer's compatibility, if it isn't plugged in to the computer.
The countdown to October 22nd continues...
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