Mediterranean areas where most of the world's figs are grown do have winters with night time temperatures below 40f and occasionally down around freezing. Seasonal adaptations surely evolved to conserve resources when temperatures drop. It doesn't follow though that dormant periods are required.
Don't fig wasps over winter insulated within mammoni and mamme crops? Doesn't that indicate that at least some figs keep growing all year?
We know from experience that we can root a cutting in late summer indoors, and grow it all winter to fruit the next summer. How different is that from a mature fig plant not having chill hours?