Player picks up a ball because he thinks it is a stray ball. However, he realises that this was his ball in play.

The player then decides to continue playing with a stroke and loss of distance.

The player's question does he receive an additional penalty stroke for picking up his ball? Yes, he has decided to continue playing with stroke and loss of distance.

Yes, he receives an additional penalty stroke. See also the interpretation:

18.1/2 - Penalty cannot be avoided by playing with stroke and loss of distance
If a player picks up his ball when this is not permitted, the player cannot avoid the penalty stroke due under Rule 9.4b by deciding to continue playing with stroke and loss of distance.
Example: A player's tee shot comes to rest in the woods. The player picks up a ball, thinks it is a stray ball, but then realises that it was the ball in play. The player then decides to continue playing with a stroke and loss of distance.

The player incurs a stroke penalty under Rule 9.4b, in addition to the stroke and loss of distance penalty under Rule 18.1, as the player was not permitted to pick up the ball at the time it was picked up and the player had no intention of continuing with stroke and loss of distance. The player's next stroke is his fourth stroke.

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