No, not just from Initiative, but some can help. Where you get less to crit % from depends on your class. For example for Chosen the best order to get it is Flawless Armor (tactic) > Futile Strikes (renown) > Armor > Initiative. Personally though, I hardly ever use Futile Strikes as I have enough from the tactic and endgame armor pieces. I do however put a bit into initiative in some builds if I have a few renown points left over after I grab the essentials.
The wiki has a good chart that explains the relationship between Ini and Crit, I like to keep mine around 250 if I can.
It all depends on your class and your play style. The current meta seems to encourage DPS classes to stack as much crit% as they can, so you need to defend against that.