OP,
You are trying to reduce a multi-variable question into a single question. The answer can easily be yes or no… depending. If you have to reduce this to the grade school level… yes, you should have a 10 gauge. But the question is far more complicated than that.
What is in front of it or behind it doesn’t matter. The only question is… if I put this power cord in, will my system sound that much better… more than enough to justify the cost? Most of the time high quality power cords made for amps will be 10 gauge… but the best sounding one might not.