Yes, you can use SFP-H10GB-CU3M to connect 6120XP to Cat 6k, with the help of CVR-X2-SFP10G converter for X2 ports. This converter will convert existing X2 based 10G port on Cisco 6500 to SFP 10G interface.
You dont have to connect to Nexus equipment. Your LAN can be anything as long as you can connect the UCS system to it.
Currently you need a switch with 10GE ports to uplink from your 6100s.
I believe that in the next version of the firmware/software in UCS you will be able to connect your 6100s to the LAN using 1G ports.