You apply no contact to avoid wasting time,resourches and self-respect on a unreciprocating girl not for raise her interest level.
It could happen that no contact gets you the chick back but its not like a collateral effect than the main one.
Anyway to answer your question, the chicks rarely initiate but when she does its mostly because she has no other options around, an in any case for sure more than a week, in my case it also needed months or in a case even a year.
It actually depends the condition of your no contact, if she is a girl that pissed you off and cutted her out while still in the dating phase, she could come back but if you go NC on a girl because she rejected or LJBFed you she aint gonna come back,she most likely dont even remember about you.
Things could be different of course if you are both on facebook and she happens to see you upolading your six-pack pictures with plenty of other chicks liking it, that would raise her interest for sure.