Is there a way to make a drill hole only up to half depth of the PCB in Eagle?
There is no way to directly do this in Eagle. You would have to simply annotate the design on some reference layer (most manufacturing data for production PCBs has some form of reference information).

However, this would be a highly customised PCB step and you would have to negotiate with various vendors until you can find one who has the capability to do this which would be exceedingly expensive ($500 or more probably). None of the pooling services (OSHPark, ITead, Ragworm, etc.) will do this as standard.

Fortunately there is a much simpler and bog standard way to do this. Surface mount PCB sockets:



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These are soldered on pads on the PCB and would allow you to plug in your module. Because they are surface mount there are no holes at all meaning you don't need some non-standard process, and you can place whatever you like on the other side of the board.