I think as long as the voltage has somewhere to go (being used to power the fan) it'll be alright to have two sources powering the same fan, but I've never used that particular fan before so if I were you I'd mock something up outside of the car & see what happens.
The relay for my fan has the thermo sensor & the A.C. over ride switch like yours, most aftermarket setups have this. I ran the A.C. over ride wire to a toggle switch so I can manually turn on the fan & it works fine, I'm sure the thermo sensor is sending voltage to the fan at the same time, but then again I've got a single speed fan.