And floatation devices are mentioned in the rules so you couldn't swim it and float your gear.
From the 2012 Nats handbook rules : 1.11 Shore fishing areas to be such that all competitors have equal chance of reaching desirable fishing areas within the times allowed and so those with beach accessible vehicles do not have an unfair advantage. The use of boats, floatation devices, special equipment, aircraft, etc, to reach shore fishing areas is not permitted.