The little 15 gallon compressor should be capable of doing something like an engine compartment but of course it depends a lot on his other equipment. If using a conventional paint gun and the lowest air pressure that will still do a good job plus working in sections then it should work just fine, people have even painted whole cars with little compressors. However if the spray gun is a HVLP type and/or the whole compartment is sprayed in one operation then this is going to be a very frustrating endeavor! The trick to using a small compressor is to accept it for what it is and properly MANAGING what air is available because nothing can be done to make the compressor put out more air than it does already. Instead of trying to squeeze more air out of a too-small compressor concentrate on spraying the most paint practical with as little air as possible while still maintaining good results.
widetrack, I see your point and I understand that if 15 gallons gave 30 seconds of spray time (it wouldn't even be that long with only 15 gallons!) that an additional 45 gallons would add more time (another 90 seconds theoretically) but that's only 2 minutes of spray time, which is probably too optimistic, and then the problems would begin. While in theory it would take 4 times as long to fill a tank 4 times as big in reality it would not work that way because as the compressor heats up efficiency falls off rapidly. On a setup such as this by the time the tank was half filled the pump would probably only be able to manage 50% or maybe even less of it's original CFM rating, this problem will only compound itself the longer the compressor runs. If this is one of the little oil-less type compressors then filling that tank a couple of times or so without long cooling periods will most likely result in destruction of the pump. I have seen it tried many, many times and adding significant extra tank capacity will almost always result in more frustration rather than solving the problem.