Dan,
No. I customarily prune my Fig trees just as they are starting to come out of dormancy in mid-April when I take cuttings for propagation. The pruning is done to maintain trees at a manageable size, take cuttings, but more importantly to stimulate new growth below the pruning cuts which will become one-year-old wood the following year.
I'm not sure it really makes a difference but if I prune right after fruiting, any new growth that starts then will be very tender and could be lost to freeze damage during the Winter. If I pruned then, my cuttings would be significantly less viable as I don't have bottom heat.
kiwibob, Seattle