No. The Frets are undercut and cantilever over the binding
Unless it's a Gibson bound neck where the frets end right at the binding and there are actual bumps in the binding that finish the profile of the fret. USUALLY, the tech talks the customer into going with the "Martin style" binding (after filing off whatever remains of the binding nibs), which is what you describe. But, if the frets haven't been resurfaced to the point the little nibs have also been lowered too much, you can cut frets to fit exactly. Unfortunately, that's rare, unless you catch a guitar that's just been played to death in cowboy chords territory and never really been dressed. A partial would be a good choice.
It's a pretty tedious operation, but if you have all the right tools, in good shape, it's not horrible. (Patience is your friend.) It used to add a good bit to the refret cost, though some folks charge the same. (I just did my mandolin a month or so ago - very short frets down there at the "florida" and *that* is a pain, though mine is scooped at the very end so saved me that!)