Place-wise it's fine, yes. Start() is called after the creation finishes.
However "tno.isMine" tells you that you own this object. If your GamePlayer object gets instantiated as persistent, and you leave, then when you come back, it will still be there. Likewise if there were two players and left, then one comes back, this player will now own both objects.
If the object was created as not persistent, then this won't happen and your code will work fine.