If you put a hero that produces 1 gildar per turn in a city with a gold multiplier, will that hero produce more gold?

I think the only way to get more gold from + gold champions is to breed them to get more +1s.

i haven't tried it in 1.09, but in 1.08b niether of the two researchers nor the gilder champion benefited from being stationed in town. there was no increase in the towns money/research, nor did i see an increase in either gilder or research equal to the bonus the unit would have got(if it just wasn't showing in the town but still being applied). i didn't see it it in the change log, so it shouldn't have changed 1.09

No, gold production is set for +1 per turn. it doesn't add to the city bonus, so you get no benefit. Although you can certainly mod something of this nature if that is your wish.