It is nearly impossible to do a copper drain pan to meet code. Code says that the waterproof layer must be sloped. If you don't have that, you are building a pan for stagnent water. It may not leak into your floor, but it will accumulate water slowly. The grout is NOT waterproof, and there will be small opportunities for moisture to accumulate there. If it was sloped to the drain, it would slowly drain through the setting medium.
I know some people think that this is the best system, and it sure costs a lot, so people think it is great, but it plain just isn't right. Ask a plumber how to slope a drain line, then ask him why water will flow out of the pan when it sits flat...if he stops to think about it, he'll probably just say, well, my pans don't leak, and I've been making them like that forever - just like I was taught. Seems more of a NE, maybe Mass thing.
Build a shower pan per the national codes - there a numerous ways, PVC liner, Kerdi, Wedi, and other waterproof membranes on a SLOPED bed. A proper tiled shower pan is made up of 5-6 layers: (lath if on a wood subfloor), presloped bed, liner, top setting layer, thinset, tile. There are ways to shortcut that, but putting the liner on the floor, flat is not one of them.
Check out
www.johnbridge.com for building a tiled shower.