The data sheet on page 10 shows the "top FET driver" at room temperature draws 125uA typical, (225uA worst case).
Assuming the MOSFETs are not damaged. Assuming the ir2110 is not damaged. Assuming the ir2110 is not hot.........
If the ir2110 was not driving a MOSFET, the voltage on the top driver will decay at a rate of 225uA/0.01uF and for a time of 100uS. That said; I think the little cap should work. Form experience if the top FET is not on well you will have a sawtooth waveform and hot top FETs.
The original drawing had errors, Some of the MOSFETs were backwards! This might kill the gates of the MOSFETs.