I didn’t do in store pickup this time, but from the last time I did an in store pickup I can tell you that apple definitely checked my ID. As long as your name matches the name on the order (which I think it would, since he used your apple ID) then you should be good. If the order was in his name then you won’t be able to do the pickup.
If the names don’t match then he may be able to call apple and add a different pickup name.