I have a Chicago Hardy that I planted in ground last year. Of course in my zone, it died back. It came back beautifully, and just now started to set fruit. Do you think they will have time to ripen?

I'd say yes.  June 1 is roughly when fruit started on my in-ground fruit in past years, so you don't seem much off schedule for your zone.  I generally started picking the Mt Etnas around the end of August, so you might have figs in mid-Sept and I'd think fairly definitely by late Sept, unless intervening weather stinks (cold and wet).  You just need the warm weather to last long enough into autumn for a meaningful harvest.

Thanks! That's encouraging. Looks like there are about 7 or 8 on there now.