Probably, if you don't medicate, and that's a solvable problem rather than a reason to abandon the trip. Plenty of people who are miserable on ferries do the Drake comfortably because they take it seriously: medication before departure rather than after symptoms, a low mid-ship cabin, and a ship's doctor available if it isn't enough. If you know you're a bad sailor, the honest options are to prepare properly or to fly across instead.
A ferry is not a fair comparison in one respect. Expedition ships are considerably larger, they carry stabilisers, and the crossing is 1.5 to 2 days rather than a few hours, which gives your inner ear time to adapt. Most people find they're fine by day two.
If you're worried, flying is a legitimate answer and it's about a quarter of the people who come to us who ask about it. What it costs you is the itinerary range, since flying rules out South Georgia, the Weddell Sea and the Antarctic Circle.
Talk to your own doctor about what to take. We're not medical professionals and neither are the guides.