Hi Drew,
Some varieties are more prone than others to show figs instead of leaves. This year i have several chip-bud grafts that are showing figs instead of leaves, like Sofeno Preto, Strawberry Verte or Lampeira.



You can remove them if you want but, usually, then don't develop much further, dry up and drop by themselves. Afterwards, the chip develops the other bud (the leaf bud) or, in some cases, stays dormant until next season.
It may be different if the fig develops in a whip and tongue graft, like this one:

In a few cases both buds develop at the same time, like in the chip in the next photo, but i never had one were the fig developed fully.
