This one's as old as the hills. Quick answer: Yes, roundwounds will damage your fretless fingerboard more than flats. However, there is not nearly as much damage as legends will lead you to believe.
From personal experience, I played untreated wooden fingerboard fretless from 89-93 (I've used all-graphite since then, and damage don't enter into the equation any more!) with Rotosound 66s (steel round). I gigged sporadically, practiced at home every day, and practiced with a band twice weekly. Through all that use, with strings that are generally regarded as the roughest you can use, I didn't have enough damage to harm my bass' playability or sound. I am a nut about my set-ups, but I never noticed a difference in feel, touch, or sound. This was on a Japanese Fender Jazz with a rosewood board, nothing fancy.
You will be able to see damage to the board (scratches, wear spots), but they never went deep enough to affect anything with me.
Bottom line, choose the strings based on the sound and feel you want. I bet any real damage will be years down the line. Worry about it the same way you worry about re-fretting: It'll be a long time, most likely.