Yes the module should pop out and have its own integrated antenna… however this antenna is not designed or tuned to function by itself, it’s designed to couple with a large card antenna that has a small coil antenna directly under the module. The whole design is meant to allow individual chip modules to be fully programmed and tested, then dropped onto a full size card and secured with glue or whatever.
Removing it from the card means that it’s no longer coupled to the large antenna it’s designed to work with and performance will be abysmal, if not impossible to get a read with.
This is why the conversion process places the module on a smaller, but still large format antenna. We don’t just coat the module itself, it wouldn’t work on its own.