Yes it will, but your only moving it a tiny bit so I've had better luck just taking a small dremel and removing a bit at a time. Than when shaving very thin wood to glue, the shavings actually have a curl to match the curvature of the hole. With a little glue it will form around the drill bit or nail. Hardest part is matching the second panel perfectly and of course not taking wood off on the wrong side of the hole, which I still do on occasion. I've tried plugging the hole completely and starting from scratch but is far more difficult and time consuming for me to get the second panel exact and of course requires removing and installing the grip pin in the frame several times.
That's how I do it anyway.