Let's see, doing a little googling here, making a few assumptions...
Boyle's Law is the key here. A
cursory web search shows about 2.4 cubic feet internal volume per tire, so 9.6 cubic feet for all four tires. Typical tire pressure is 30 PSI gauge, or ~45 PSI absolute. Let's make things simple and assume the air is being released to atmospheric pressure, which is ~15 PSIa.
So:
45 PSIa * 9.6 ft^3 = 15 PSIa * volume of released air
This gives us 28.8 cubic feet of air when released out of the tire.
Next step is to apply
Archimedes' principle and figure out how much water gets displaced by 28.8 cubic feet of air. We'll go with
62.3 lbs per cubic foot of water.
62.3 lb/ft^3 * 28.8 ft^3 = 1794.24 pounds of displaced water.
So, if my ballpark math is correct,
that's only a little more than half of the water you need displaced. So sadly, in spite of your impressive efforts, your car is doomed to sink.
Please kindly correct me if I'm wrong about any of this.
Edit: Crap, I forgot to add in the water displaced by the car itself. But I'm tired, and I'm not terribly sure it'd work.