I was able to get a room at the Columbia club via the housing portal a month or so ago. I notice they have a "strict" dress code.
Do they waive it during Gen Con or do I need to pack a few suits?
I've never stayed there, but check out this thread from a couple of months ago. It should answer your questions.
They will ask you to obey the dress code if you're going to hang out in the public spaces of the club. But that code isn't actually very strict in terms of what to wear. No ripped jeans, no spandex, no hats, etc. No cell phones in public spaces either, FYI.
But if you're just coming in and going to your room, you're fine. They know what the con is and what sort of guests to expect.
That said, if you have the space to bring some nice clothes, it can be a comfortable and quiet space to hang out :)