Yup, you can go classless. As a conceptual foundation, Adam and Sage have said (though I can't find the exact link & quote right now) that you could start with your class and just pick from all the moves, and the game would work just fine. Why it works is because moves don't really ever give you more power, they just back some of your existing fictonal choices with a new degree of consistency. When you understand moves in that way – they're consistency insurance – suddenly moves look a lot more flexible and mungible than they at first appear in the book.
The design point of classes is to reinforce theme and niche – but not every game design needs niche protection for characters, and theme is something that you can develop in other ways. Theme is particularly important for *World games, in that it's not nearly so optional, because it establishes fiction and the establishment of character fiction is essential as a foundation for your players doing fictional positioning. (And *World games are all about fictional positioning: doing something is about building up the fiction to put you in a position to pull off the next thing you want to do.) Classes implement theme in an easy way: here is your playing piece, here are your customisation options, here's the resulting heavily-suggestive, evocative character to start with.
It sounds like you're researching in order to do a moderate-sized hack on Dungeon World. So long as during development you keep in mind the issue of niche protection – that is, do you want it in the first place and if so, does your moves-tree design generate it – you'll be fine.
Theme will be harder to implement, but not impossible. You just have to make it a design goal of your hack. In a tree system you can embed theme in the branches, effectively moving the bits of fiction that make a person who they are out of the class structure and into the branching choices. If your branch bases are heavily fiction-laden, then they will effectively serve the same thematic role as classes in normal Dungeon World, acting like combinable mini-classes. Take the enchant-my-gear and the sharpshooter branches? You've got something that feels like an arcane archer. Take the heavy-defense and melee-smash trees? You've got a wrecking-ball knight thing or something like that. The videogame Skyrim works this way, and the resulting characters are extremely evocative and indistinguishable from traditional classes.
So, yeah, be aware of what classes do for Dungeon World in-play, consider how much of that you need to preserve, and roll it into your moves-tree design. Go for it!