Attacking RSA signature verification that ignores padding
If you were using $e=3$, then there is a well known attack by Bleichenbacher that enables the trivial generation of a signature that passes verification. This attack was never published, but is described here. Note that this attack appeared in a real vulnerability in Kindle (and some versions of Android).

In any case, the attack does not work for $e=65536$. However, if your question is whether or not it's OK to use this, then it certainly is not. The existence of the $e=3$ attack should be enough to convince you of that. On the other hand, if your question is constructive to find an attack, then I don't know - but it's a great research question.