Yes it works with flimsy sleeves. Not with premium quality though.
This is true, however the flimsy sleeves still do a reasonable job and protect the cards fine in my experience. That's the sacrifice one needs to make to keep it organized in one box. And I'd rather flimsy sleeves than no sleeves at all. Mind you, I take pretty good care of my games and have that many that it probably wont get a huge amount of playtime in the coming year, maybe a few games if I'm lucky. Even my favorites only hit the table maybe 4 times a year, so your millage on cheap penny sleeves may vary.