Not really, compare the strength of a coke can that has been shaken up (under pressure) to an empty can. Can under pressure is much stronger. So you would think frame air pressure would have some influence on frame strength if only in certain directions.
The mine I used to work at, pressurised dragline booms that were made out of tubular steel up to 130psi and the machine had an interlock that would not allow it to operate if the pressure was too low.
As for racing teams filling the tyres with nitrogen/helium, I think it is to prevent the chemical vapours that are released from the rubber when running hot from reacting with oxygen (ie Exploding). Same thing happens in large mining trucks when the tyres get too hot.