Peonies are pretty hardy, I imagine they will be back in the spring. Whether they will bloom, I don't know. If he cut them back right after flowering, they didn't get the sunlight/nutrients they need for future blooms, so they may not bloom well, if at all. And of course, that is provided he didn't add an additional spray of roundup to kill the weed.

They won't grow back this year; peonies' grow period is done after blooming. There's no reason to think they won't come back next year, though. You can help by fertilizing with an organic bulb fertilizer, BulbTone works well IMO. Just add a teaspoon or so each and scratch it into the soil around the peonies. I'd make sure to educate your landscape guy, though, for next year!