What would be the extent of the feedback on climate of unattended deaths event?
Mass of Earth's atmosphere: $5 \times 10^{18} kg$

Concentration of methane in Earth's atmosphere: $1866 ppb$

Mass of methane in Earth's atmosphere, present day: $9.3 \times 10^{12} kg$ = 9,300,000,000 tons

If all those dead mammals were composed entirely of methane, they would increase the atmospheric concentration of methane by about 2%. They aren't, and (as @trond hansen commented) most of their carbon would be converted to $\ce{CO_2}$ with a 30-fold smaller global warming footprint.

So, I think it's safe to say the impact of decomposing mammals would be relatively small.

Worry more about effects on plants, which constitute 80% of the Earth's biomass; bacteria, which constitute 15%; and fungi, which constitute about 2%. The entire animal kingdom amounts to much less than half a percent of global biomass, and half of that is arthropods (which have their own concerns for the future).

(Source: figures from The biomass distribution on Earth, Yinon M. Bar-On, Rob Phillips, and Ron Milo, PNAS June 19, 2018 115 (25) 6506-6511; first published May 21, 2018 https://doi.org/10.1073/pnas.1711842115)