I think it can be done, although some parts will be harder than others.
As some have already stated, giving assault rifle-wielding squadmates the Typhoon will help. Does not matter what difficulty, since they can tear through a lot of enemies with it pretty quickly.
There are some segments where you will have to shoot/use powers though. Off the top of my head:
- On Vancouver before leaving Earth. Anderson does not starting fighting along side you right away, so you will have to kill some Cannibals by yourself.
- "Dr. Eva Corre". Should be self-explanatory.
- Omega DLC, when fighting through the trap at the Reactor. It has been a while, but I think there is a part where Nyreen stops to help Aria and you are left by yourself for a while. Not sure if it is time-based or enemy-based but you will have to fend off mechs for a while. Also, in the run to the Reactor console, there are Rampart mechs and Cerberus Troopers trying to stop you. You can probably just run by those, though. Omega DLC is optional.
- Omega DLC, final fight. You will have to shoot Aria out of her restraints. Omega DLC is optional.
- Husks and "Marauder Shields", assuming you decide to actually finish the game at this point.
- Citadel DLC, some Armax Arsenal Arena challenges require you to solo. These are completely optional in the Citadel DLC, which is also optional.
- Cain on the Hades Cannon on London.
Also the following squadmates can reliably detonate their own combos:
- Liara (Singularity > Warp, also Stasis > Warp)
- Javik (Pull > Slam, also Dark Channel > Slam)
The following can also detonate their combos, but with less reliability:
- Ashley (Disruptor Ammo > Concussive Shot, Inferno Grenade > Concussive Shot)
- James (Incendiary Ammo > Frag Grenades/Carnage, Carnage > Frag Grenades)
EDI and Tali can also detonate their own combos, but only due to extreme luck. Requires Explosive Drone/Decoy exploding at just the right time.
Toughest fights in this type of playthrough would probably be:
- Brute spam at the end of The Shroud.
- Three Geth Primes on Rannoch.
- Clone fight on Citadel DLC. Citadel DLC is optional. Which class would the clone be easiest?
- Maybe the Brute spam + Harvester on London defending the missile battery
- Two Banshees on Ardat-Yakshi Monastery maybe? I always have squadmates die here. This mission is optional, though.