mIP certainly does process ARP packets. But, there are 2 components to mIP. The TCP/IP stack and the driver. The only driver for mIP is written for the enc28j60. To use mIP with another controller, a driver for that controller would need to be written.
Do you have in mind to modify mIP so it uses the J11D?
I don’t think this is a simple Task, if even possible. At least it’s not just changing some pins, because ENC28 is a SPI device, builtin Ethernet is, well, builting. J11D is not much more than the RJ45 connector.
as Valkyrie-MT wrote you would need to replace the ENC28 Driver for mIP by one that accesses the builtin Ethernet.
To do so you need to disable the builtin Driver. Not sure if this would work.
Also mIP is pure managed, builtin Driver is part of the Firmware.
By this mIP is slower. To my knowledge you can also not use Socket, and other standard network classes when using mIP.