No, they will send you the sensor grid and you have to remove the old one and put the new one in.
The grid lives under the cushion and I have never heard of anyone getting the cushion with the grid, otherwise that would probably cost a grand or so knowing M/B.

The job is not bad if you pay attention.

It helps to remove the entire seat from the car, then remove the seat back to access the part and flip the seat over and over while fiddling with it.

Pay attention to how the wires are routed and you will be pleased how easy it really was to do.

If you are halfway descent mechanically, you will do fine.

You probably have set a code that will not go away until a SDS is put on it to clear codes.

If you repaired a broken wire,and that was the only problem, you may just need the code erased with a laptop.