When a bowler over-steps, resulting in a no-ball, and the batsman's wicket has been disturbed with the ball going to the boundary, then 5 runs are awarded to the batting side. Five runs is split as one for overstepping and four for the boundary. All these 5 runs go into the extras (no-ball) column. However, if the ball touches the bat/glove before hitting the stumps and then goes to the boundary, 1 run is added in the extras column for the no-ball and 4 runs are added to the batsman's score. Either way, the batting side get 5 runs.
The delivery that immediately follows the no-ball (overstepping) in limited overs cricket is a free-hit. This means that the batsman cannot be dismissed in any way apart from a run out, handling the ball, hitting the ball twice or obstructing the field. So, if the ball hits the stumps and goes to the boundary, the batsman is not-out. Instead the batting team get 4 runs as extras (byes) for the ball reaching the boundary. If the batsman has nicked the ball before it hit the stumps on its way to the boundary, then all 4 runs are awarded added to the batsman's score.
Long story short, if a batsman gets bowled off a free hit and the ball goes to boundary, then YES, 4 runs will be added to the batting side.