No, magic won't heal or buff all units. Even if it does heal, it's only a small part. Anti-magic is needed, and it's ESPECIALLY needed for Nature.
Firstly, it removes curses. Nature, I note, doesn't have exorcism. And if Order casts "Forgetfulness" on the elves? What will they do then? Just stand around doing nothing, to be slaughtered?! And if they summon mantises (or something else), and Order wants to eliminate them with "Banishment." And if Chaos starts splitting phoenixes? What will they heal or buff?!
Realistically, when anti-magic isn't needed is in a battle against Life. Here, in my opinion, there will be competition to see who can buff their units the most. Life, of course, has a significant advantage here. But that's a completely different story...
P.S. Everything I described applies to the Anti-Magic spell, for those who didn't understand. It's really only needed for one (or at most two) units. And the Nature mage, I assure you, will have plenty to do. There will be someone to buff and heal (if they have the Blessing of Life in their spellbook!).
Maybe I just don't know how to use anti-magic, but it NEVER helped me; it always just hindered me, and I've already explained why...

Барон "Vampires"
Отдай свои прошлые сны,
В сомненьях себя обрети,
В бешеном танце душа кружится!
Не думай, что будет потом,
Здесь и сейчас мы живем,
Стань хоть на миг сам собой, слышишь!