Quick answer
Yes, but the Atlantic sits at 18 °C, about the same as a cool English pool. Most visitors swim in the sea-fed lido pools or natural pools on calm south-coast days, or in a heated indoor hotel pool. Lifeguards are off duty until mid-June. North-coast pools (Porto Moniz, Seixal) often close on Atlantic swells.
Context
Sea-surface temperature around Madeira bottoms out in February and March at roughly 18 °C. That's swimmable for cold-water regulars and fine for a quick dip on a sunny south-coast day, and the sea-fed pools at the Lido or Doca do Cavacas in Funchal make an easy, sheltered place to do it. They are seawater, not heated, so for warm water pick a hotel with a heated indoor pool.
Wind and swell matter more than temperature. South-coast spots (Funchal, Câmara de Lobos, Calheta) stay calm most of the winter. The north coast is exposed to Atlantic groundswell, Porto Moniz and Seixal natural pools often close for safety on bigger days. Check the live sea state before driving over.
Pack a 2 mm shorty if you plan to spend more than 15 minutes in the water; locals don't bother for a quick swim, but visiting Northern Europeans usually find it noticeably colder than expected.