The two NICs in the R610s are totally separate... So, if one goes bad, the other one will continue to function.
Now, to answer your specific question:
No, the Broadcom controller chips do not provide fail-over redundancy.
Having the multiple NICs does allow for that functionality though. You will simply need to configure a NIC Team. A NIC Team is a logical device made up of multiple physical NICs. The NIC Team has the IP Address, Default Gateway, etc.
There is a Broadcom utility available (I believe gets installed when the correct drivers are installed on the server OS) and there is also NIC Teaming functionality native within Windows. I personally have had stability issues with the Broadcom utility, where the native Windows configuration worked great. HP's NIC teaming utility has been great for me though.
Setting up a NIC team is generally pretty simple, as mentioned in this post