While the system will still function without the antennas on the tags, we would not recommend removing the antenna as that causes a significant loss of range. There should be no other impact on performance other than loss of range, but the loss of range is very significant. Without an antenna, we expect the maximum range on the DWUSBs to be reduced to little more than a few meters. You are obviously more than welcome to test this setup to see if the severely reduced range is still sufficient to meet the needs of your project, but unless you are working over a very small area, it is highly unlikely that the antenna-less DWUSB will be able to suit your needs.
Removing the antennas from the tags does not require a recalibration.