The other possible problem is that the hot water outlet usually
contains small air bubbles, which usually go up the open vent pipe or
out of the HWS taps. The air is dissolved in the cold water and are
released when the water is heated. Connecting the pump to the HWS
outlet pipe might allow these bubbles to accumulate in the low level
pump & cause an airlock.

I'm fairly sure that your proposal wouldn't comply with the pump
maker's installation instructions and could invalidate the guarantee.
You can usually get the instructions off the web sites. I'd plan on
fitting an Essex/Surrey/Warix flange.