Is it possible for phoenixes that have detection to be able to pick up burrowed swarm hosts to kill/neutralize them?
Well, phoenixes can pick up borrowed units, so I guess swarm hosts don't count as different
See here: wiki entry for phoenixes
... Burrowed zerg units will be unburrowed by the ability, and will reburrow when they fall back to the ground...
Yes, it is possible.
They tested this is the following youtube video: SC2 Mythbusters Episode 1