Well, I think most common transformations work reasonably well. One usually doesn't want to do things completely contrary to the AST, such as convert "while a<b" to "whilea = b".

And it's certainly possible to create any valid AST in the editor I describe. The set of valid trees is extended to those with "holes" in places, which one fills in when entering a program, and it's always possible to do this.

The challenge is one of finding an intuitive user interface, not whether it's possible at all. One issue is that infix notation is unnatural for entering trees (prefix is more natural).