I'm kind of surprised no one suggested mud jacking.
I haven't heard of what you are talking about before, but it seems it should work.
Check out mud jacking first though. It may turn out to be a lot cheaper and easier than what you are planning. The idea is to drill holes in the old concrete patio, then pump gravel and cement under the slab, lifting it up to the desired height, then refilling the holes. It has several advantages over what you are considering.