I think your chances of them ripening is pretty good. I would not leave them out in the hot sun. Those dang goats. When we had ours we had a big locking latch that they could pick, so we also used a big bungee wrapped a few times. Sometimes we would let them out near the garden if we were out and one would sneak up to the front and maybe grab a radish but we would shoo them away. They were a great way to high speed compost though, especially broccoli leaves and stalks. No roots.
and it's ready for the garden as soon as they drop it. I usually let it age a little at least. I have a few buckets of it right now. I started four shisitos a few weeks ago and transplanted into a 50/25/25 mix of potting soil/very aged chicken coop soil/goat manure and they seem to be loving it so I might get some after all. They're in a pot so I can bring them in when needed and when outside, they're too high for the goats to reach.
Pretty sure I have the goats and LGDs sold as a package deal. Losing my shirt but if I can't keep them fenced, it's not working. I might do some work on the fence this winter and get some hair sheep next year. They're easier to fence and lamb is yummy. Not trying to do anything with the fence right now because I'm a tick and chigger magnet. I have years old scars on my legs from chiggers. That acid they secrete to soften up your skin really effects me.