By rule, a player can't gain control and shoot with 0.3 seconds or less left. BUT, a player can score with a tap.
Art. 19. In any period, when the game clock displays 10ths of seconds and play is to be resumed by a throw-in or a free throw when 3/10ths (.3) of a second or less remains on the game clock, a player may not gain control of the ball and attempt a try for a field goal. Such player can only score a field goal by means of a tap of a pass or of a missed free throw.