See summary. Given that illager beasts are equivalents to iron golems, which are mobs that don't drown, it doesn't make sense, unless there is proof that beasts aren't artificial mobs like the golem.

How to reproduce:

1. Make a 3 x 3 x 3 hole
2. Cover it with a ceiling
3. Fill it with water
4. Spawn an illager beast

          →  It drowns after a while, eventually dying after a long time due to its massive HP.