The altimeter will freeze if a blockage occurs but that would be in the static system. The VSI would read zero. If the pitot gets blocked, the ASI behaves like an altimeter and will increase its readings as you climb. If the static gets blocked, the ASI error will reverse, i.e. it will under-read as you climb.
At least that's what the JAA questions expect - real life has nothing to do with it!
The water drain is usually operated with a spring (every 200 hours on some aircraft), so that implies some sort of seal. It would have to be sealed in normal circumstances (like the alternate static) otherwise the readings would never be correct.