Can I piggyback a thermostat with a C Wire hookup on a furnace?
I also have a thermostat that requires a C wire hookup for wifi access.  The spec calls for a 24 volt DC and I presently have it wired to share a 24 volt termination on my AC air handler.  What I discovered was that this termination in the air handler does not provide a constant output of 24 volts.  Instead, it cycles as called upon by the air handler and the thermostat would run until the battery failed which took about a month.  Plus I could not get the wifi to properly pair with the thermostat due to the cycling of voltage on and off to my C wire termination at the thermostat.

This afternoon I have an electrician coming to give me a dedicated wire from a 24 volt transformer for my C terminal.  I expect this to solve my problem.

So based on my experience, be cautious of sharing unless you know the source will provide constant power.