Can I use this simple ethernet pcb header with arduino by just plugging it into a breadboard and routing the pins to the arduino digital pins?
No you wouldn't. You need to purchase a shield or adapter... They can be had for as little as $5usd to $10usd.
So like this one right: http://www.ebay.com/itm/1-2PCS-ENC28J60-Ethernet-LAN-Network-Module-Schematic-Arduino-SPI-AVR-PIC-LPC-/251472502315?pt=LH_DefaultDomain_2&var=&hash=item3a8cedde2b
Also, out of curiosity, what does the shield do exactly other than break out the pins. What does the IC on it do?