No. A remains A until the end of the play; B remains B until the end of the play.
EDIT (added as FLAHL made the post below):
As mentioned here (
http://www.refstripes.com/forum/index.php?topic=11985.msg119589#msg119589), there are 10 "major clock stoppers"; if one of these occurs, the clock starts on the snap:
a - the ball goes out of bounds
b - B or R is awarded a new series
c - either team is awarded a new series following a legal kick
d - the ball becomes dead behind either goal line
e - a legal or illegal forward pass is incomplete
f - a request for a charged, or radio/TV, timeout is granted
g - a period ends
h - a team attempts to consume time illegally
i - the penalty for a delay of game foul is accepted
j - a fair catch is made
None of these occured. Wind it up.