You can also check in at the Dawson Trail pavilion on French Lake anytime after 2 pm on the day before your put-in. It's a half-hour drive east of Atikokan (maybe out of your way), but the Atikokan office closes in late afternoon (4 or 4:30), while the Dawson Trail info centre stays open until (I think) 7:30 pm.

You really do want to pick up your permit  in either Atikokan or at Dawson Trail the day before you go in. Not only is the Beaverhouse station a bit out of the way, but you also run the risk of arriving after a big group, and having to sit and wait while their paperwork gets done.