I'd argue that a starship would be as likely to maintain a "natural" orbit as a modern oil- or nuclear-powered naval vessel would be likely to tack into the wind.
If, instead of being slave to Newton, you can
hover over a planet in a pattern of your choosing (and any starship worth the name can), then you will
do so. It would be pretty silly to revert to a Newtonian orbit even once when you are likely to be using "powered orbits" and complex tactical patterns 50% of the time anyway. I don't think Sulu would ever choose a natural orbit unless explicitly told to do so - perhaps so that the ship could masquerade as an asteroid or something. It just wouldn't occur to him, any more than it would occur to the helmsman of an aircraft carrier to use his ship as a sailing vessel, even when conditions allowed for this. Sulu's natural instinct would be to fight the (insignificantly feeble) forces of nature, not to go along with them.
It would take a "special" pilot, perhaps somebody fanatically interested in esoteric "naturism" of some sort, to actually bother with freefall orbits unless there's a specific need.