That depends. If the fig is already getting soft it will continue to ripen off the tree as it is already producing ethylene  gas, the stuff that helps ripen fruit. You can speed the ripening by placing the figs in a paper bag with a ripe banana. The banana gives us the gas that helps the figs to ripen.  The figs that are still firm and green may not ripen off the tree as they are just too immature. Keeping your fig tree well fed and watered will hasten ripening and having less fruit and shorter branches means a shorter ripening time needed. Stressed fig trees take a long time to ripen the fruit and often frost arrives before they are ripe. You may also want to consider a covering of tulle cloth to keep the birds and bees at bay. Keep growing, Marianne Binetti