Yes, they can survive and produce.

This happened to me as well last summer. Freak wind storm came out of nowhere and ripped a couple limbs off my blue tomato plant that had blossoms and even some small tomatoes on it. My first time growing a blue, and I really wanted to keep as many as I could get, so I potted the torn limbs up and hoped for the best.

Those limbs not only survived, but the fruit that was on them survived, and they continued to produce for the rest of the season.

Wasn't covered in as big of fruits as the ones on the main plant, but they were producing. Didn't even use any kind of rooting hormone, just stuck the torn end in some potting soil and crossed my fingers.

It'll look like they're wilting and dying for a while, but just keep watering them normally and they'll bounce back.