No, if anything plant-eaters are less healthy because they have a less diverse diet.

Ideally animals with a fairly high energy budget need to be omnivores, like for example humans. If you look at animals of comparable weight, all the herbivores are ruminants, or woefully unsuccessful.

Even fairly small horses, for example, have a really bad time trying to get enough nutrition from their diet and if they eat a tiny bit too much or too little they pretty much just die an agonising death from stomach problems. This is after thousands of years of us trying to breed the strongest healthiest horses we can, incidentally - the very earliest horses were the size of cats and lived for a year or two at most judging by the fossil record. Even at the dawn of agriculture horses were horribly fragile creatures.