Nope. Absalom rebelled against David. Solomon is not mentioned in connection with him.
Adonijah, another son of David, attempted a couple of coups against Solomon, but they did not get to the level of civil war. Solomon executed him after the second attempt.
Is the Old Testament the same in every version?
Ahitophel, who sides with Absalom (he is the one who suggests that Absalom sleep with David's concubines) but later commits suicide when his advice is rejected, was the grandfather of Bathsheba...so the great-grandfather of Solomon, who would never have reached the throne if Absalom had succeeded David.