Can I put a Y fitting into the wall to accept two p-trap drain assemblies? I need one for the Reverse Osmosis system and the other for the double sink with disposal.
Yes, in most every home, multiple P traps eventually go into a single drain. The important considerations are that there is proper slope, there's a vent within a certain distance of the drain (either wet or dry), and that the drains are properly sized. What you can't have is one P trap in line with another (creating an air locked section), but two P traps that connect to a Y and enter the wall should be perfectly fine.
I would use a wye to separate the 2 drains from the double bowl sink. That is what I always do on a double bowl sink. Then, use a slip nut branch tailpiece with a rubber reducing coupling (with hose clamps) to tie in your R.O. drain. Never use compression tees on kitchen drains; they have restrictions in the tube that often allow clogs.