Cana snails will mow down your plants in very short order as I learned that the hard way. I had a nice cave covered in java moss a while ago and got 2 cana's and within a week and a half I had no more moss on my cave.
But my brigs have never eaten my plants as far as I can tell. I have willow leaf hygro, java moss, java fern, guppy grass, and hornwort and they always crawl around on my plants but I have no holes or eaten parts on any of it. I can't say they haven't ever "tasted" it but with all the snails I have my plants still grow very nice and look very healthy. It is funny how I can put a romaine lettuce leaf in the tank and almost every snail is on it and eating within 1/2 hour but they don't eat my plants. Same with duckweed.
I just got the willow leaf hygro about 3 weeks ago and it is in my juvie snail tank with probably 75 brigs and it still looks as nice as when I got it. Maybe if they don't have anything else to eat they will resort to eating live plants but most of the time they only eat the dead/decaying leaves.
Maybe applesnail.net would know for sure.