If I tie into a 6/12 pitch roof with 2x6's. Will I be able to span a concrete slab of 11' 6"? I will be setting 4x4 post every 6' with 2 2x6's with 1/2" osb sandwiched between them as the form to set on top of post. My plan is to add 2x6 supports on to the top plates of the existing house wall where the 2x6's intersect with the walls.
It looks like the answer is "probably not." If this calculator from the American Wood Council is to be believed (and if my assumptions about your materials and load are correct), the max span is about 10ft for a pine 2x6.
This table agrees that 10-12ft is the max span for typical grade lumber, at typical spacings, for a 5psf dead load.
While your particular circumstances might come up with slightly different numbers, I'm going to bet that you're in the vicinity of the max span for that material. How closely you want to shave that risk is up to you.
That's a long span: if you go that length, you must block it every four feet, which you need to do anyway for nailing the plywood. Do you get a massive amount of snow? If so, you may want to go to 2 X 8. If not, the patio roof only bears it's own weight, and the block stiffens the joists dramatically. The other issue is the building code: if you're pulling a permit, they will have the final word.