Choose the rules you like :
BCA
5.6 PUSH OUT
The player who shoots the shot immediately after a legal break may play a push out in an attempt to move the cue ball into a better position for the option that follows. On a push out, the cue ball is not required to con-tact any object ball nor any rail, but all other foul rules still apply. The player must announce the intention of playing a push out before the shot, or the shot is considered to be a normal shot. Any ball pocketed on a push out does not count and remains pocketed except the 9-ball. Following a legal push out, the incoming player is permitted to shoot from that position or to pass the shot back to the player who pushed out. A push out is not considered to be a foul as long as no rule (except rules 5.8 and 5.9) is violated. An illegal push out is penalized according to the type of foul committed.
After a player scratches on the break shot, the incoming player cannot play a push out.
VNEA:
D2.
If the cue ball is pocketed or driven off the table, or the requirements of the
opening break are not met, it is a foul, and the incoming player has cue ball
in hand anywhere on the table.
F. PUSH OUT. The player who shoots the shot immediately after a
legal breakmay play a push out in an attempt to move the cue ball into a better position for
the option that follows. On a push out, the cue ball is not required to contact any
object ball nor any rail, but all other foul rules still apply. The player must
announce his intention of playing a push out before the shot, or the shot is considered
to be a normal shot. Any ball pocketed on a push out does not count and
remains pocketed, except for the nine ball. Following a legal push out, the incoming
player is permitted to shoot from that position or to pass the shot back to the
player who pushed out. A push out is not considered to be a foul as long as no
rule is violated. An illegal push out is penalized according to the type of foul
committed.
APA : Push outs are apparently not allowed (That's what I read... never played by those rules before)
And of course the rules Patrick posted.
Seems to be an overwhelming no.