Sure, it's possible. The sequence of multiplications chosen to reach the exponent is different, so these expressions take different paths through scm_integer_expt.
But the sequence of multiplications chosen to reach the exponent isn't different. What the user's expt function does, when asked to compute (expt 2 488), is to compute (expt 2 244) and then square it. When it computes (expt 2 244) it does the exact same sequence of multiplications as if you just asked for that directly from the REPL.
What am I missing here?