You can route your Ethernet Signals out from the cortex a9 to the PL, however you will not be able to send the signal back to the Ethernet Jack on the PicoZed FMC V2 Carrier Card as that Ethernet Jack is routed directly to MIO Pins.
However, there is another solution!
Avnet has a Network FMC that would plug into the FMC connector on your PicoZed. http://zedboard.org/product/network-fmc-module
The Ethernet PHYs are connected to PL pins on the FPGA, so you can route your Ethernet signals out to the PL, do any tasked need be, and then properly connect it back up to the Ethernet PHYs on the FMC.
As of now we only have a single reference design for this FMC module featuring the UltraZed-3EG, please take a look at it and see if it will fit your application. Please reference UltraZed PCIe Carrier Card + FMC Network + lwIP http://zedboard.org/support/design/17956/141