Can you put a through-hole part behind an SMT part?
The hole for the connector would be near the center of the MCU package, away from the pins.


This is a very bad idea.

Usually the pins from through-hole parts stick through the board by at least a millimeter, more than enough to interfere with the ability to place a chip where it would cover the pin.

You could conceivably cut the pin short enough that it doesn't stick through the board, but that's going to be a special operation and add cost. You wouldn't be able to inspect the solder joint with the through-hole pin because it would be all hidden in the hole. 

It will also mean the chip has to be hand soldered because it has to be attached after the wave solder step is done to solder the through hole part.

If you had to rework the through-hole part, you'd have to remove the chip, rework the through-hole, and then re-attach the chip.