There's a couple mods out there that change the player character's appearance. Would I be able to tie a mechanicus model with a specific class?

Try it and see? I have no idea if it will work or not. I can't test compatibility with every mod out there 🤷‍♂️

I did check and it isn't compatible. But I'm actually asking because I'm trying to create a patch myself but I couldn't find where your mod is interfering. Choosing a class switches me from the mechanicus model to a normal engineer. I was hoping your mod directly changes my character model so I can just change the pointer. I can't find anything though, do you know where the change is happening?

I don't modify the default character. I create additional characters.
https://github.com/modded-factorio/bobsmods/blob/main/bobclasses/prototypes/character.lua

Does the creation require you to assign them models or animations?

It copies the base character model

Is that the line data.raw.character[character.name].animations = util.table.deepcopy(data.raw.character.character.animations) in data-updates? If so then I think that's what I'm looking for. CharacterModHelper I think makes a similar table.

Does this mod support alternate character appearances?

TLDR: Yes, kind of.

More detail: Bob's Classes already interacts with my character switcher miniMAXIme. If both these mods are active, miniMAXIme will create new character prototypes (versions respecting class properties) for each recognized alternative character provided by third-party mods. Thus, the animations of alternative characters will be used for all classes if miniMAXIme is active. If no selector mod is active, the animations for alternative characters will only be available for the "Balanced" class.

Caveat: There are other character selector mods. I don't know whether they are compatible with Bob's Classes as well.