Not necessarily. For truly random events with a known probability (like a coin flip or a die roll), the percentage of X over a large enough sample size should converge to the probability of X. So past percentage = current probability.
That isn’t true for a three point shot. The probability that a player will hit his next three point shot is not static from shot to shot. There are too many factors that go into a three point shot for it to be a truly replicable random event. Steph Curry in an empty gym is as close as you are going to get.
Shooting percentage is at best an approximation of the probability a player will make an individual shot, and for some players a very rough one at that.
We can come up with a much more accurate picture when we factor in location on the floor, who is defending, time and score, and yes, how hot or cold the player has been recently