I'm pretty sure you only need to use the clock pin, the MOSI, and the MISO and you would use SPI which would be more stable than the UART. The address and data pins are only needed if you're interfacing to the module using an external memory interface (like pretending that the chip is RAM to a chip with a memory controller). At least I'm pretty sure this is the case, as would seem to be implied by page 10 of the datasheet:
WIZ811MJ provides following interfaces of W5100.
-. Direct/Indirect mode bus access
-. SPI access
And because it says interfaces instead of interface, I would assume you could use either one. That being said I've never used a wiznet module so I have no idea