Consequence of a change on the Guillou-Quisquater Protocol
Yes it proves that $y \ne 1 \pmod{n}$ is not an $e$-th root. That is, no $x$ exists such that $x^e = y \pmod{n}$. In particular, if $e | \phi(n)$ then for any $x$ it holds that
$\left( x^{ \frac{\phi(n)} {e}} \right)^e = 1 \ne y$.

This probably means one last final conclusion designed as a homework.

Regarding GQ protocol: prover will be unable to pick an $r$ such that
$a = r^e \ne 1$.