Aerodynamics, EO viscosity and your right foot makes a much bigger difference to FC. Spare tire more for handling. But considering the number of times it's happened to me or I help ppl at the side of the road, I would bring it with me. Even go further and only buy car with full size spare (getting rarer these days).
Pulled over to help this family in a Jazz Hybrid going to the airport. Ask where the spare they give me this electric inflator, but they dunno where the wire that powers it, dunno how to use, we just stand there like idiots. Anyway useless la the inflator, no way can last even 10km.

Also spare tire is designed as part of the sound dampening of your car. Removing it will make your car louder inside.