Provided the concrete slab is strong enough to bear the weight of the completed deck, I'd pour my own piers on top of the slab. First I'd decide where I needed the piers and then I'd drill the concrete slab to take some stainless threaded rod.
When building an elevated deck, if you have small children, consider installing a child gate or railing or tiny people will fall. The front view from the deck. View from the elevated deck
Estimate the amount of wood required First of all, you have to find the amount of wood you need to build the raised deck, and to do this you will have to make a plan or design for the deck.
So, having never done a raised concrete deck, I started sniffing around and came up with a plan. Here's what I have: Deck is just below slab level. Brick ledge is three feet down. So we bolted a 2x12 ledger at the proper height to the slab. Poured a footing 8' off the house. Double 2x12 beam sits on 6x6 posts every 4' on said footing.
You can do this in such a way that all of the concrete is hidden under the deck. Then put on a lattice skirt or build the wood down to the ground to hide it more if you like. Your idea would probably work ok, but this is more of how a builder would do it.
I am planning on building a raised concrete patio. I would like to build the perimeter of block and fill it with stone and then cap it in concrete to be finished with blue stone later. The patio will be about 3 ft off the ground and jogs in and out but basically 40 ft long and about 12 ft wide.