You would like to know the noise spectrum on the supply,
and beat that against the PSRR-frequency curve to see
what kind of output noise will result.
A faster bandgap might reject, or pass noise, depending
on its rolloff. Remember that the "forward" frequency
response and the supply-output response are different,
and once the loop begins to fail to null it you are at the mercy
of raw feedthrough.
My preference is to post-filter bandgaps against the reference
ground, rather than depend on a "sporty" amplifier to kill
on-chip noise sources. Pre-regulating with a slow dumb
well-filtered LDO can help too.