Does google maps use elevation to calculate travel distance?

I doubt it. Since the length of a sloped road would be sqrt(1+x^2)-times the length of the flat one (where x is the slope). For low values of x, this is roughly 1+1/2*x^2, which is rather low, eg. for a 10 % slope, you get an error of 0.5 %. Not considering the actual lane you drive probably has a similar error.

Even a very steep 10% grade is only 1/2% longer than a flat road covering the same horizontal distance.