Well the actual dripping lines wouldn't be good for sheetrock but I love the idea of an automatic way to water house plants. Maybe a drip line would work in tiled sunroom attached a faucet.
I have put all my plants in the bathtub and soaked them and left a bit of water in the tub before traveling. Also there are ways to recycle bottles into drip watering systems for potted plants. Plants are like pets and need care but they are worth the effort.

I would think setting up connection points to the regular plumbing in each room would be no trouble for a good plumber. Then it's a matter of hooking up valves and drip lines as needed.

@MrHIrrigation - Thanks for the encouragement. What kind of valves would you recommend? If there is a way to automate a system, that would be ideal.

just like any irrigation system I would set it up with electric valves and a standard irrigation clock.

My personal choice would be to use Rainbird valves and clock.