It is really important especially for toxic attributes you receive from Gordy Goop since it lasts almost 15 seconds. If you’re playing Imp and you catch a Goop from another player, it can be a nightmare surviving for 15 seconds and receiving 35 damage upfront.
Also, the stuns you receive from Engineers aren’t always full stuns. Some of them could be less because of how they are spread around and also the fact that some of them might’ve been destroyed (you can shoot those things if you didn’t know that already).
Buffs do have an activation sound but that's about it. I wish there were more visual indicators to how much damage % I'm getting buffed or how much HP I just received. Some upgrades reduce the damage received and it would be great to know the duration since it's not mentioned anywhere.
So, yes... Adding those icons would benefit players in planning their next moves carefully. If they are about to die from toxicity (not from the players', but their abilities =p) then they could spawn a healing bot or a spawnable ally. If I knew when "Reduced Damage" is about to end, I'd try to find cover before the effects end.
This would also assist players in knowing whether those effects are working or not. (In some cases, certain upgrades might not work as intended. Knowing when they got activated and when they ended would help players and the developers diagnosing those effects.)