This sounds about right. You are not pumping a lot of water great distances, so the maxijet and RO tubing connecting through a John Guest fitting to a Y dishwasher drain will work. I like the suggested valve/pump operation as well.
You need to be careful about where you drill the hole. Sometimes DWV systems defy what seems logical. It is possible that there is a vent line for the sink drain that runs in the wall vertically above where that drain enters the wall. It is also possible that the drain line may run horizontally from where it enters, depending on what other fixtures it was connected to (are there tubs, toilets, showers in the same room?). There are standard approaches to how these things are plumbed, but you really never know.
It would be best to do a little investigating before you drill the hole. You could locate the studs by tapping on the wall to listen for a change in sound, or shining a flashlight along the wall looking for places where screws/nails attach the drywall to the framing. You could also carefully remove a small square of sheetrock where you plan to drill, just to get a look inside the wall.
How do you plan on getting replacement water in to the tank?