Is an airless paint sprayer recommended for painting kitchen cabinets, boxes and doors?
You can use an airless sprayer but stay away from the inexpensive models.Consult your paint supplier if thinning is required. The one problem with spraying indoors is overspray and fume buildup in other areas of the house.If it is possible remove the cabinet doors,(mark them so you can tell where they go) and drawers. Mask off the garage floor and plug in a fan blowing out. This will keep the wind and overspray to a minimum.The face frames and cabinet sides can be done with a roller. Make sure you use an approved mask or respirator for the paint you are using.
You could but I would never recommend it. You'll probably end up with a lot of runs and sags. There's too much volume with a airless and you need to keep your movements fluid and quick this is difficult and in some cases impossible with cabinets.
You should be looking at an HVLC if you want to use a sprayer. I would recommend renting a good one over purchasing some cheap thing.
One thing about Mike said the fan thing could be a very bad thing. Be aware of how close your neighbors or cars are. That paint being blown out can end up traveling with out drying (depending on material and weather). I can't tell you how many guys I've seen accidentally paint a house or car. Even dry paint will bake on to a car in the sun.