Yes, str influences skill crt chance.
But it's not worth it on a dagger. MAYBE on an aw since he already has high str, but meh. Nobody does it for pvp. I do it for pve, and with a pl set I really crit very often (I just need the patk from str though). But I sacrifice con for that, so... Only good in ganks or mass pvp (large scale).

@Benebain. By what you said, you can add a song of wind, and your final speed will be 173. With blinding blow add 40 more speed. But it lasts 15 secs and you need a target.