Yea it will continue to run for a while, but we all know what longterm underfuelling does to headgaskets and pistons the switch is the SOLE component that triggers the full load enrichment.

As for thw running fault, my first RST had an issue with not pulling properly in higher gears which i seemed to dissapear when i fitted a new TPS - the old one was knackered but i wasted £40 on a new one cos i pulled the old one apart and it only had dry solder joints inside