Buds use the energy the fan leaves produce so with that reasoning I'd assume that cutting off the bud would increase growth in other bud sites although being a tiny low light bud site it wouldn't be very much

Cutting the fan leaf off wouldn't hurt very much either cause again it's a low light site but if it's just hanging there all shriveled and brittle you could probably just remove it...

This next part I'm not sure about so it's either one of 2 things...

1. The energy the fan leaf produces can be ported all over the plant which means you should cut the bud and leave the leaf as it will help the other buds a little...unless the leaf had some sorta spreading infection or whatever I'd leave it

2. The energy the fan leaf produces can only be used at the bud site it's connected to or some limit there in...which would mean if you chop the bud you chop the leaf

Logic makes me think it has to be 1. but if someone knows otherwise feel free to post