Actually, no. A lop-ear vaporeon’s ear can still drain just as a normal vaporeon’s ear will.

However, that doesn’t mean that lop-ear in eevee isn’t a cause for concern. While water can drain rather easily from a vaporeon’s ear (Note: It might not for eevee, however, so please be careful about letting your lop-eared eevee swim), bacteria is an entirely different story, and lop-ear is a prime breeding ground for microorganisms due to the fact that the opening is held against the head (thus providing warm, moist shelter). This means that all members of the eevee family except flareon are highly susceptible to ear infections, so eevee with lop-ear must be checked regularly for any issues.

As a note, the reason why flareon is exempt here is because it possesses the capability of raising its body temperature (and withstanding higher temperatures) than is viable for most strains of bacteria that would cause infection in its cousins and preevolution. For this reason, flareon is actually resistant to most ailments, simply by virtue of simulating an intensely high fever for a short period of time.

For all others, especially the fragile leafeon and the normally aquatic vaporeon, it’s important to keep your pokémon’s ears clean, check inside their ears regularly for any signs of dirt or pus, and keep an eye on your eevee or eeveelution for signs of infection (lack of coordination or balance, fever, pain, difficulty hearing, and so forth).