You can not tile over live circuits. The only way you could do this would be to pull back or deactivate (abandon) the existing wire in the backsplash and route it (or install new circuits) to the plugmold.

Sure they can! UC lighting should be placed towards the front of the cabinets and hidden by the light rail. Plugmold goes at the rear. They are on separate circuits, not the same circuit. If you have conventional framed cabinets, the wire for the UC lights can be dropped down between the air space between the cabinets while the wires for the plugmold emerge directly from the wall. If that's not possible for your electrician to route it that way, then the wires can emerge from the wall at the rear and be covered with a cord cover (paintable to match your cabinets) until they reach the light's box or the transformer for the lights. I'm really not sure why he's having a problem with this. It's not the most comforting thought that he doesn't know how to do this.

Our backsplash is the same as the counters -- Neolith. We will have one low, horizontal wall outlet on the other wall where the coffee maker/toaster will be plugged in. The wall where we are considering the plug mold has the range, fridge and a short run of counters. There won't be any appliances plugged in here permanently so no risk of hanging cords.

@theotherjaye - one thing I forgot to address in my previous post is your OP statement "lighting angled back at the front", The UCL needs to be placed toward the front of the upper cabinets, and also pointed straight down. As I said above, you want the UCL lighting to light the center of the counter beneath it. If you have the UCL "angled back at the front" you are ruining its function of lighting the middle of the counter beneath it. The lights need to point straight down. Are you getting a light rail attached to your upper cabinets? Even the slimmest UCL benefits from a light rail. Since you need to send the designer this thread, ask about that too.