No. Merely returning to an onside position is not enough.
Once a player is determined to be offside two things must happen to fix it:
1. That player must get back to an onside position
...and...
2. a team-mate must touch the ball, an opponent must control the ball, or the ball must leave play.
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No. A player can never be in an offside position while on their own half.
A player could be in an offside position in the opponent's half at the time of the touch, run back to their own half to collect it, and be guilty of an offside offense. The officials would wait and see what the player did once they were determined to be in an offside state.
A player on their own half of the field cannot be in an offside position, and therefore, cannot be called offside. However, this determination is made at the moment the ball was last played by a teammate. This means that a teammate can pass the ball forward, and a player who is in an offside position can cross back to their own half and collect the ball, and will be called offside. The location of the restart will be the player's position when the teammate played the ball, i.e. on the other half of the field. This is known as an "over and back" offside call. This type of call is fairly uncommon, particularly near midfield, but it can and does happen, especially at youth levels.