Bricks, Masonry, Asphalt and Concrete - Concrete patio drain (drainage)

Well the impossible happened – money started growing on trees (actually a nice anticipated tax refund). So now I am researching to finish off the last of my backyard projects – build a BBQ/Bar area in a space about 14x14. It used to be a play area complete with rotting wooden structure for kids. I wouldn’t let my kids near it. My problem is that I will now lose this as a drainage area. My raised concrete patio is already fitted with a drain that goes to a professionally done hole (French drain?) in the middle of my lawn.
This area is not so lucky. My question is – is it possible to build a drain hole (of course filled with crushed rock, lined in fabric, etc under a slab of concrete? Currently, I have an approx 20x20 roof section with a downspout that will need to drain somewhere. It currently hits a concrete walkway and the new slab will tie into the current one. In Northern California (San Jose), while we get rain, it’s not like a massive thunderstorm. Tying into the lawn drain is not an option either.
Any thoughts? I am trying to avoid standing water, etc…thanks all!