It's biased, but I think Doc is just BARELY viable. I think the tiers go Falcon, then ICs just ever so slightly ahead of the next 3 characters with them being virtually tied as far as viability is concerned.
- Pikachu
- Samus
- Doctor Mario
I think Doc has a lot of tools that keep him at level that's just barely acceptable in the current meta. He shares a lot of similar tools between Sheik and Falcon. His up air combos are okay, but are easier to escape than Falcon's. His d-smash is VERY good, his punishes off of grab are great, his punishes off of low percent crouch cancels are decent, his movement is super slick and his back air is fantastic.
As I'm sure you know, even though you're asking if he's viable, he suffers from a drastic lack of range compared to a lot of the higher tier characters. He has short limbs and has some of the least disjointed hitboxes in the game.
It's very, very difficult for Doc to get in on camping space animals, campy Sheik, bair heavy Puff, a Marth that focuses on walling out, and a fair focused float cancel Peach. All of those matchups are definitely winnable as Doc, but are still really hard to win.
I might be missing a few notable character matchups, but that's generally why he's placed where he is in the minds of most players in the Melee community.