It does if you reduce the domain to positive integers, taken advantage of the problem being quadratic on all vars:
s = Solve[a^2 + b^2 - c^2 == 0 &&
0 <= a < 100 && 0 <= b < 100 && 0 <= c < 100, {a, b, c}, Integers]
ListPointPlot3D[{a, b, c} /. s]
