Going from personal experience... I say absolutely yes, though I imagine it depends on whether or not your queen bed is a standard queen, and of course, whether or not the queen-size sheets are standard as well.
Full disclosure: I have a queen sized bed and a memory foam mattress, but before I went the whole nine yards with the memory foam, I owned a standard spring mattress with a memory foam topper that was about 3 inches thick.
I have to say the fitted sheet was a "little bit" tougher to put on than before, but it worked. And I got used to it, so by the third or fourth time I had to re-fit the fitted sheet, it was second nature. The covering sheets fit just fine, but I feel like those are usually designed to hang several inches past the mattress on either side, anyway.
Overall, I think you should have no problem using your current queen size sheets on a queen size mattress with a memory foam topper!
I hope you enjoy your topper... I know I loved mine! And maybe someday, you can upgrade to the full memory foam bed. Oh wow, so heavenly! :D
I hope this helps.