There are probably a lot of opinions about this. My opinion is that he is.
But one thing I am sure of is that there are two clues in the movie. Their inclusion into the movie plot indicate that the creators wanted you to conclude that Little Forrest is in fact Forrest's biological son.
When Forrest first finds out about being a father, he asks if he can be with Little Forrest. He goes over to him, sits down, and they both start watching TV. From that point on their actions are identical: They get caught up in the show at the same time, AND they tilt their heads slightly to the left at the same time.
Later on, we see that they both love the same things naturally. Little Forrest loves to fish. Once again they get caught up in the sitting "action" of fishing with their heads tilted slightly to the left.
Please observe this YouTube clip that shows the father and son tilting their heads to the left. Forrest, the father, goes to his son at around 4:20 minutes; they tilt their heads at around 4:38 minutes.
In this YouTube clip, we see at 1:11 minutes that Little Forrest has a knack for ping pong. At 1:18 minutes, both father and son are fishing and again have their heads tilted slightly to the left.