Having the full set doesn't make you invincible to gloom...though it is a BIG help. What each piece does is give you one...well, I think of them as 'heart protectors'. So if you have the full set, you have three protective hearts. The gloom 'breaks' your hearts each second you spend in it, so you have several seconds of walking through gloom 'free', as the armor absorbs that and those hearts break in place of your actual health. Then as soon as you are out of the gloom, they repair...unlike your real hearts, which will only repair if you get to a lightroot or go to the surface. (Link in the depths is me in winter versus me in summer, lol. I, too, have my heart dramatically healed by sunshine.)
My set is upgraded only once, since I'll have to fight 9 freaking froxes to upgrade it to level 2 to get the bonus, but knowing it'd be such a pain to upgrade, I decided to look up what you get out of it other than higher defence, but the set bonus at the second fairy upgrade doesn't appear to make you invincible to gloom, either. It simply gives you a fourth protective heart, and since they heal as soon as you get out of the gloom, they really are very useful and let you walk through all but the biggest patches of the stuff without worrying.
Basically the set makes it so you can be significantly less wary of gloom and gloom-ridden monsters, but it nowhere near makes you invincible, unfortunately. I was hoping that, too, and if it had, I'd have gone to the bother of killing all those froxes for it. But for a fourth protective heart, each of which lasts one second of gloom-walking? Nah. Though froxes are easier than taluses, so there's that, at least.
Overall, I've found the Miner's set more useful to exploring the depths than the Depths set, although the Depths set is strangely adorable and the Miner's set is strangely disturbing, like a glowing lightbulb clown + S/M kink + plague doctor. Put it all together, and you're not sure just what kind of kink Link is running. I also have the Dark Link set, but it can't be upgraded (ARGH) so the defence is terrible, and I don't like sets that make Link look like other games' versions of him, it looks so jarring in this game world and I prefer he just looks like this world's version of himself, so I'll probably never use it...it only has the same bonus as the Sheikah set anyway, which you can upgrade and thus has much better defence. Oh, I mean the 'stealth' set. WHY DID THEY RENAME IT?? Why does the existence of the Zonai mean the devs had to try to erase the Sheikah's contributions to the world? Bad world-building, Nintendo!
As of yesterday, I have over 2/3 of the depths mapped...84 lightroots of 120. My tendency to: 1) climb everything 2) glide as much as possible rather than walk and 3) avoid all battles, works really well down there. Not for gathering stuff (other than zonaite from the un-abandoned mines, where there are no enemies anyway) but it's great for finding lightroots!