Possible? Yes. Simple? Oh no. The ESP-IDF example makes a modification to the SDK settings (here). The Arduino uses a precompiled version of the SDK with this setting set the opposite way. So, integrating it into Arduino-ESP32 would require a recompilation of the base libraries which I presonally found to be extremely tedious (GitHub - espressif/esp32-arduino-lib-builder).
The ENC28J60 is a very common Ethernet chip with good general library support. Do the libraries linked at Ethernet test on esp32 not work?