Depends.
The problem is chronology. We have to reconstruct peacemeal narratives from disparate sources, as already noted.
Some have argued, most notably David Rohl, that Labaya from the Amarna letters is Saul. This requires a massive realignment of traditional dates; which Rohl makes based on a rising of Sirius and equating Shisaq with Ramesses instead of Shesonq, but that is a different argument. By traditional dates Labaya lived in the 14th century BC, but by Rohl's chronology he is in the 10th, close to Saul's probable time.
Anyway, Labaya's activities somewhat mirror Saul's. Both of their kingdoms are centred in Samaria around Gibeah. He also named his son Mutbaal which is a close etymologic cognate to biblical Ishbaal and both these 'men of baal' sons moved their centres of power to the transjordan area after their father's death. Mutbaal's letters also mention figures that might be David, Joab and Jesse based on similarity of names. It is an interesting theory, but remains speculative without more support for Rohl's chronological revision. We must remember though that the dates of near eastern history are far from set. While Rohl's chronology has a lot of problems, there are also problems with the traditional Egyptological dating. The truth probably lies somewhere in the middle. Dating sometimes changes, as an example the fall of Nineveh has been redated 4 times in a 150 years since Assyrology first investigated the matter.