i do that mostly with KTV girls.
but it's not to get to know the girl.
it's just to fill up my stomach...
in your case, it depends on what type of WG you are with.
for walk-ups / HGs, i think you can't just call up the WG and say "hey, let's grab some sandwich."
u can do try buying some food when before u go up to the 141 flat or hotel, it can definitely help to break the ice.
once you are a regular customer of the WG, then you can invite them out for a candlelight dinner.
if you are hitting on bar girls, you can bring them out for supper first.
except for the cost of the supper, i think no extra costs will be incurred.