Absolutely not. Empiricism has no place in judging the validity of mathematical propositions!
Rather, it would testify either of two things:
a) The measurement was false
b) The measurement is correct, but the conditions required for the appliciability of Gauss' theorem are not present. (I.e, you have a case of misapplication)
Which of these would be the right one in your particular case, I don't know.