Is building a Slime Hutch worth it?
If you spend a lot of time in the Caves or Skull Cavern, it's probably worth it. Green, blue, red, and purple slimes have a 1% chance to drop an egg if a Slime Hutch has been built -- this is the same chance as a Slime dropping a Diamond but that's relatively common considering how many slimes the player will encounter.
--- Can you water crops inside a Slim Hutch? ---
No, sprinklers will not water Garden Pots regardless of their location.