Uncomfortable and dangerous aren't the same thing, and the Drake is mostly the first one. Expedition ships on this route are ice-strengthened, carry stabilisers, and have a doctor aboard. Forecasting is now good enough that captains route around the worst systems rather than pushing through them, which is a genuine change from how this crossing worked a few decades ago.
What you should expect is motion, not peril. Things slide off tables. Walking down a corridor takes concentration. Some people are miserable for a day. Those are real, and worth preparing for with medication you take before you feel unwell.
If a crossing does turn bad, the standard response is to slow down, alter course, and wait it out. Losing a few hours is normal. It's one of several reasons expedition itineraries carry slack in them.