No. However if you do not change any of the parameters and the function does not involve random variables, then the second call would give the same result as the first call.
fsolve does not modify any of the input parameters.
I do sometimes see people using code such as
x = [0,10]
x = fzero(SomeFunction, x0, x);
and then get surprised when they try to use x as if it were still the vector instead of having been replaced with the specific solution.