Hey DTB...i just noticed this thread...i don't have my onboard air set up right now, but when i tested it, it ran my air tools just fine. My big ram bumpers and rock sliders are my air tanks, though...their internal space is probably equal to a 30gallon shop tank.
The compressor CFM should surpass your air tools CFM...just one tool at a time, of course. The air tank just lets you use the air tool for longer periods before the compressor kicks in. With a tiny compressor you'll wait forever for it to pump the tank back up. With the high output of a York compressor you can use your tools and air up tires without worrying. Electric tools are ok, but they're heavy and they overheat...air tools cool themselves. An air-powered drill is probably the largest air consumer. I like my 625 ft. lb. 1/2" impact wrench...try finding an electric one that powerful.
Here's a pic of my engine on the stand, with my York compressor mounted...i went to a semi-truck dismantler and bought 2 compressors for $40.00