You can if you like, but it's more bother than it's worth as the existing PnC connector on the controller works out much better for that, especially if you plan to keep the 360 board intact like I've done. It's just a USB connection with 3 extra pins for the charging circuit of the PnC cable to charge the 360 controller, just don't even bother with those 3 pins and wire up the 4 you need for the USB connections, and that's about it, you have a connector that's already there and can use any PnC cable for the USB cable to charge it, the PnC cable doesn't have to be modified in any way at all.
If ya want to go installing the miniUSB connector from the controller that can be done several ways, making a hole in the controller somewhere and gluing it in place, pulling the pins from the PnC connector and cutting it out to fit in there and securing it, etc., etc., but ends up being more work that using the existing PnC connector, plus looks like arse IMHO.