I have solar with an MPPT controller, and currently the old, crappy single-stage convertor. They don't seem to fight each other, but the plan is to swap to a 4-stage converter to get better performance on shore power.
I see from the solar current display that if the converter is running, the MPPT controller basically goes to sleep, and does not push any current into the batteries, based on the voltage it sees. My solar is wired direct to the batteries.
(On Edit: TheGreatleys have the simplest answer for the real situation...)
Rich, KE4GNK/AE, Overkill Engineering Dept.
'The Silver HamShack' ('07 International 22FB CCD 75th Anniversary)
Multiple Yaesu Ham Radios inside and many antennae sprouting from roof, ProPride hitch, Prodigy P2 controller.
2012 shortbed CrewMax 4x4 Toyota Tacoma TV with more antennae on it.