Yes, but the drawbacks are that
you cannot steer the development
you cannot enforce compatibility
you cannot ensure that your users are happy (unless your users are your developers)
You most certainly can steer development of your own fork of ANY opensource project.
You are not required to continue down the path of the main branch. Hell for that matter the dos.library of MorphOS is a fork of the dos.library of AROS. looks to me they controlled the direction they wanted to go with it pretty well(they are now very different). I could list some other parts used by MorphOS or AOS4 but I'm lazy.
