  While Primordial Black Holes (PBHs) with masses $M_{\rm PBH} \gtrsim 10^{-11}
\, M_\odot$ cannot comprise the entirety of dark matter, the existence of even
a small population of these objects can have profound astrophysical
consequences. A sub-dominant population of PBHs will efficiently accrete dark
matter particles before matter-radiation equality, giving rise to high-density
dark matter spikes. We consider here the scenario in which dark matter is
comprised primarily of Weakly Interacting Massive Particles (WIMPs) with a
small sub-dominant contribution coming from PBHs, and revisit the constraints
on the annihilation of WIMPs in these spikes using observations of the
isotropic gamma-ray background (IGRB) and the Cosmic Microwave Background
(CMB), for a range of WIMP masses, annihilation channels, cross sections, and
PBH mass functions. We find that the constraints derived using the IGRB have
been significantly overestimated (in some cases by many orders of magnitude),
and that limits obtained using observations of the CMB are typically stronger
than, or comparable to, those coming from the IGRB. Importantly, we show that
$\sim \mathcal{O}(M_\odot)$ PBHs can still contribute significantly to the dark
matter density for sufficiently low WIMP masses and p-wave annihilation cross
sections.
