You are talking about NIC teaming to create a "port-channel"in network terms, or "Ether-channel in Cisco terms,
If you have two ports connected to the same access switch and a compatible network card its certainly theoretically possible. They often do this with servers.
It depends how locked down your unis switches are configured.
You will probably need to configure a virtual "team" ip accross the 2 nics as well
worth a go though.
I should point out if your connection to the switch is 1 gig, and the uplink form that switch to the next is only 1 gig you wont gain anything, though unis dont tend to cheap out on networks so you may be in luck. Alos if you do get it working it will depend what form of load balancing the switch uses. I think the default on cisco kit is to split the traffic based on the source mac ir IP address, if all of your traffic is going to the same address, again you may see no benefit.