If you only and exclusively use the DLC characters, I suppose so, but I don't see what's stopping you from using generics at any point. You probably want to at least create a mage/skull and/or a healer pupil* for your spellcasters, otherwise you'll be stuck with the characters' innate skills (usually 3 in total by level 50+). Again, that is mostly an issue for spellcasters, the others will learn weapon skills normally (weapon mastery in staves increases dmg, range and aoe of spells, but you don't learn the spells themselves from it). Eventually you'll also want to create a thief to steal items, since otherwise you'll be stuck with 50% chance for stealing at most. You should also consider including a few knights in your party just for their throwing stat.

*Just in case you don't already know, you can learn spells (Fire, Star, Heal, (de)buffs etc, but not weapon or innate abilities like Hurricane Slash or Crimson Flame) by having a master stand next to their pupil and cast a spell they have until you reach lv 1 with that spell for your master (now they can cast that spell on their own, without needing to stand next to their pupil). Conceptually it's a bit weird that the master learn from their pupils, but whatever.

With that said, the bonus characters are pretty good in general, with stats and aptitudes close to generics of tier 5~6. The only trap character afaik is Bridget, the alraune NPC in Holt Village.

Thanks for the detailed answer. Just so I understand, though, at early levels this means I'll have to create a pupil for my spell casting DLC characters, of every variety, go into a battle, cast the spell until I learn it, and repeat this every few levels when a spell becomes available?

I mean I'll do it, but it seems like a really silly system that doesn't add any enjoyment to the game.

Well, higher tier mages/skulls learn multiple elements (do know that they don't learn the highest tier spells, only the base/specialized mages/skulls learn those), but to unlock them you'll have to level the pupil(s), which I don't know how inclined you are to do it. Also, you don't need to have all elements on one character, one (maybe 2) is enough. Just watch out for enemies that are immune to an element - Dragons, Mystic Beasts (wolves) and Aqua Demons (slugs). In that regard, star magic is the most useful since it can't be resisted (but it might lack in power later on).

A game mechanic that I neglected to mention (and I believe it's exclusive to D2) is that your elemental affinity not only helps reducing the elemental dmg you receive in general, but it also raises the elemental dmg you deal with your spells of the respective element (again, only spells, not abilities in general). For example, any Red Mage/Skull you create will naturally deal higher dmg with fire spells while dealing poor dmg with ice ones (if you teach them any). This isn't very important for the "DLC" chars, since they are neutral to every element, but it's something to keep in mind if you eventually give them specialists that raise elemental affinities or decide to use generics as spellcasters (generics always have +50% in one attribute and -50% in another).

Lastly, you can even consider not getting the higher tier spells (at least during the main story). I've heard that, at least in D1, the difference in power of the lowest and highest tier spells is only about 20% (maybe 25%, it's been a while) at the same level, so by the time you unlock the peta spells and such, your base spells will be doing more dmg, not to mention that they'll have higher range and aoe options. You can focus on getting the higher tier spells later on when you have the means to both level the pupils faster (for them to learn said spells in the first place) and have farmed some Mentors to level the spells faster.

Beware, you can't use unique characters from Adell Mode in Axel Mode. Try to get a high level generic attacker before starting a new cycle.

I have no idea what a "cycle" is. :\

Another word for "playthrough". This, like most (probably all?) disgaea games, features new game + (starting the game again, but with things like characters' levels, equips, HL etc carried over). What Z3n alluded to was that, after you finish the main story, you get to play a side-story with Axel (or, if you want, replay "Adell mode").

you only need axel mode for its play through and the dark world playthrough.