"I wonder what the likelyhood would be of finding a permit available at a particular entry on any given date, without a reservation? I have actually walked in and picked up a permit at Prairie Portage in early September without a reservation.  I was prepared to camp in the BWCAW adjacent for a day or two, if it took that before there was an opening.
It seems that Cache Bay and Prairie Portage and LaCroix are less busy than the Canadian permit stations overall.  Anyone have any statistics?"

depends on what date and what entry point, obviously

statistics, no  but I have changed my entry date to one day earlier the past two years when entering at Nym Lake when I had a reservation for Memorial Day (I changed to Sunday, - I use Monday to have a cuhshion if my travel time is longer than expected)

In 2006, I just showed up at Dawson Creek one day, and asked about getting a permit for the next day.  I was told that there are always two permits available on a first come, first served basis for Pickeral Lake entry point - and I was told to just show up early in the morning, be first in line, and I would get one.  And I did.  unless something has recently changed, I assume you can still do that -

I have not received a call back yet from the phone call reservation I made several weeks ago.  Due to other concerns, I'll probably not pursue that original reservation plan, but will just be winging it if I go this year, and hope for a permit  to be available thru Atikokan/Nym lake, or use one of the two first come - first served Pickeral Lake permits.  At worst, I might have to wait a day, I'd guess, for an opening.  I wouldn't try that in mid-summer busy season, unless I was flexible enough to go for a mid-week entry date, which ought to increase the odds of an opening.