To re-phrase the question, what constitutes a false start?
The NFL rules are discussed at NFL.com. In short the center must keep his head stationary for one second. This time restraint necessarily lends itself to a bit of ambiguity and judgement call from the referee. The rules also mention intent.
So in actual practice the center must have all parts of his body stationary for a brief moment before hiking and none of his movements should be "abrupt" with the intent to draw the defense off-sides.
The NCAAF official rulebook has the same language under Rule 7 Section 1: The Scrimmage - Shift and False Start (pg. FR-71).
The 2014 NFHS official rulebook also has the same language under Rule 7-2 Article 7 (pg. 58) with an emphasis on intent.
To your question:
Technically the center must halt his motion but the rule books leave plenty of leeway for the referee to decide. The intent to draw the defense off-sides is the most significant aspect of the ruling.