Alacrity is a damage-boosting stat, nothing more
This "nothing more" should not be taken too literally. I think alacrity can have some small contribution to survivability at least for shadow/assassin tanks. Speeding up their attack rotation means they build up to 3 stacks of HS/HD that much faster allowing them to get that self healing that much more often, so it would little bit increase their HPS.
Now don't get me wrong, I'm not saying that alacrity would be good enough to be worth using in your gear. I'm planning to remove it all from mine. Just noting that despite being undesirable stat, its contribution to survivability would not be 0.