When attempting to solve a gravitational potential energy equation, is the free-fall acceleration always 9.8m/s2?
No. It depends on how far from the Center of the Earth one is.
g= forcegravity/massaccelerating= GMassEarth/distance^2 where distance is from the mass to the center of the Earth. Now if one is on the Earth's Surface, one senses a constant g. But if one goes up 1000 miles into space, g is different.