I'm experienced with the w5100 and w5200 versions of the ethernet library, and I do not see where the arduino or wiznet library code is involved with an arp broadcast. I think that is done by the w5100 firmware internally when it establishes the connection.
The w5100 doesn't have a bunch of internal SRAM. Most is taken by the 4 socket buffers. It doesn't leave much for arp lists. 