Are you sure? What makes you think that?
I've never tried, because I find that the Lynels do too much damage unless I'm using my highest defense armor (especially the higher level ones), so even if I have a lot of HP upgrades and only get hit a few times it's still enough to waste a lot of high level food making it not really worth it.
And my highest defense armor happens to be the ancient armor.
But there's no indication in the game at all that the effects don't stack, so that's why I'm wondering what makes you think that.