Sure, it's technically possible. But not common from the projects I've seen.

The APIs seem to be designed with the assumption that all your code will be using jQuery. For example converting a wrapped node to a native DOM node requires an extra call that, in my opinion, is ugly: $('.something').get(0); and could be considered to be an anti-pattern.

I don't think this is a bad thing. jQuery does a good job at providing a DSL that replaces native DOM access. But if you want a library instead of a framework its strongly opinionated style can be off-putting.