Big hit 2 chainstay design
Pretty sure this is the frame in question, maybe different color, but the reason this won't generally work applies to most designs.

The chainstay link is connecting its dots in 3 dimensions, not just 2. In other words, it's not flat; the distance from the pivot to the frame centerline is a different, larger number in back then in front. So even if the way the hardware interfaces wasn't an issue, which for most frames it would be, you can't just flip it upside down because it won't connect the dots right anymore.
Say you were asking a similar question but more from a fabrication standpoint; i.e. you were thinking about making a new chainstay link that did connect the dots but took a little different path for clearance reasons or whatever. Generally that's fine if you make it strong enough, design it right, etc. There are various full squish frames with very different looking pieces left and right.