For me, at least, I think "pickup" (and "pickup line") has something of a negative connotation. An "ice breaker" seems more neutral. It's about getting things started, not "sealing the deal".

I also think "pickup lines" tend to be ascribed more to men. Maybe "ice breaker" would also be a bit more gender neutral (if you are interested in marketshare in both genders).

P.S.: I'm both a bit older and a bit of a wallflower, so my perceptions may be off.