No, surely the parity is virtually 100% certain to catch the error...??
The only way it wouldn't is for more than the one bit to be in error
in such a way that the parity becomes valid again.  If bit errors are
so rare, it's an unlikely situation, so the parity bits should be a
good test.  However, it's so rare, and parity bits themselves can be
subject to error, I wouldn't bother with it.  They don't either!
Karl