I'm more wondering about the upper register here, but I suppose this applies to pedal notes also. Is the trumpet's range theoretically unlimited? Is there anything (besides the player) that potentially could limit the range of the trumpet?
As Matthew indicated in his comment, once the wavelength of the sound gets smaller than the diameter of the tubing, the trumpet will no longer behave like a column of air. This means that, at these wavelengths, the trumpet will not support the resonance modes that make up its behaviour at normal frequencies. I.e. not sound like a trumpet (to the extent that it sounds at all).