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Here is the thing ... a cop can (not saying they will) arrest you for DUI if you fulfill all of the following requirements.
1. in / around your car or motorized vehicle
2. are intoxicated
3. have your keys on you
Considering you will most definately be partying at IF3, sleeping in your car after getting nice and toasty on the magical nectar that is alcohol, can potentially be a problem.
If you are willing to risk it, there are parking lots all around montreal that are cheaper than a hotel and can house your car for a full 24h. Also, not directly downtown but in the vicinity, you might able to find a 24h Tim Hortons or McDonalds (or something similar) where you could crash in the lot.
Last suggestion would be to park at the Casino de Montreal. The parking lot is large, is free and 24h. If you guys aren't attracting attention to yourselves sleeping in your car (building a campfire, etc.) I don't see why security would find or even hassel you. You could go park there and just hit up the metro nearby to take you to the festivities. The only problem I see there is that the metro stops running at around 1am (give or take), so getting back to your car / sleeping spot might include a lift, taxi ride or damn long walk.
You could always just park at the casino to sleep and drive yourselves around the festivities as parking on the street downtown is free after 9pm on weekdays and 6pm on weekends. But try not to drive when you're on the "sauce".