not really IMO because there's basically only major 1 conversation duel, and it's not even that important. you can win it without the aug if you just use advice you picked up around town (that he's arrogant but also a bit vulnerable) but it would probably take a couple tries. but even if you fail it, i think you can still just break into his vault anyhow... there's a window you can access from outside that also gives entry to his back office, and you can probably just hack his vault.
there's a few other small places you use the aug (couple of them only have a single interjection response) but they're really pretty minor... it's nothing like DX HR sadly where there were a number of conversation duels that had pretty important results (e.g. the Sarif one which you cannot get any other IIRC).
as for augs... invisibility camo and the Smart Vision are huge for stealth... for combat, probably the armor and health to begin with because without them Adam is kinda a glass cannon... even on medium difficulty you die pretty fast again later enemies, like barely a few seconds sometimes. i don't think quiet walking is important if you have invisibility but if you were doing non-invisibility stealth then you'd probably want it because you have much less of a window of opportunity so the extra speed is useful.
energy battery boosts were really big for me in stealth because i was basically always low on energy from always using Smart Vision, but I have to add that I play the game mostly HUD -less.... so the 'interactive item' highlight is turned off.. so I use Smart Vision often to double check rooms to make sure I got everything. if you play with the full HUD, maybe a stealth build really doesn't need as much battery as I did because I turned off that part of the HUD.
telsa kinda sucks imo... the pathfinding for it is horrible... half the time i try use it it, at least one of them get stuck on a barrier or something. situationally it's awesome when you got really open LOS but it's so rare that i didn't get to use it much and often i just decided to get up closer and do a double takedown and then quickly stun gun the third target if need be. when you set up that perfect 4 person takedown it is pretty cool but i genuinely rarely used it... and probably the last two times i tried to use it, it kept missing (even when i reloaded and tried over and over) because the enemies were standing on a bridge... and because the tesla bolts kinda twirl.... they don't shoot straight but they twirl and arc around, one always seems to get caught on the waist level bridge or a wall edge.
it feels like something designed by the art team (woah this twirl looks cool) but was never tested for practically lol (which is how most of Adam 2.0 feels... kinda dislike how flashy superman most of the augs are, but that's a different topic).
heavy lifting is huge... if you explore, get both heavy lifting and hacking 5. you won't really enjoy heavy exploration if you can't heavy lift and hack, and also break down walls, because so many cool little things are hidden behind them. gas breathing is the least important for those, i felt it was the least common barrier. still enough to justify it but i didn't personally get it.
then... Icarus Dash is also kinda nice for stealth because i used it a lot to access bridges or ledges, and bypass enemies... enter apartments, etc. but it's loud and it can alert enemies, so it's more for exploration or pre/post- enemy infiltration (e.g. after you stealth past enemies and you're hidden in a corner, it's safe to use) but not really useful to use while actually stealthing near enemies. it's not super loud but it did alert enemies (based on noise, not the vision detection meter) a few times for me.
if you do aggressive combat though, i'd probably bypass a lot of these and just make sure you get a lot of defense upgrades and probably that slow motion reflex mode or whatever. you could probably take less hacking too cuz if you kill everyone, it's a lot easier to find keycodes from lower security devices haha.