In Hawaii (zone 12a), nearly all of my fig trees go dormant mid December until mid April. If the figs are just starting to form, they will probably all fall off before they ripen. If they are close to ripening, they can still ripen without leaves. I usually lose 50/50 after the leaves drop off.
It's probably better for the tree to remove the figs, since it saps the reserve energy the tree has to ripen the fruits without leaves. I only leave on a few figs that are closest to ripening.