In the NBA, Rule 6.I.e.2. shows
Ball entering basket from below
As an infraction that awards the other team possesion of the ball. So if this happens and the referee blows the whistle to call it out or even indicates that this infraction occurred after the fact, then the ball was dead and so the ball falling back in the basket does not count for points.
Same in NCAA and FIBA. The moment the ball enters the cylinder from below, it’s the same as going out of bounds. Play stops and the ball is awarded to the team that did not touch the ball last.
No it won’t be counted as it’s considered a ‘violation’. Ref will blow the whistle stating as such and the ball will be handed over to the defending team.
RULE 9 - VIOLATIONS AND PENALTIES Section 6. Travel, Kick, Fist, Through Basket from Below A player shall not travel or run with the ball, intentionally kick it, strike it with the fist or cause it to pass through the basket and enter the cylinder from below.