You could do NIC teaming and get 10gb/s overall (on the network link - idk how they route USB/NIC/PCIe/etc.). You wouldn't get that on a single connection that way, though. You'd have to either be content with multiple connections, or not team them and use a multi-path aware protocol like iSCSI.
I'm curious how close your total throughput would be to the theoretical 10Gb/s, assuming it was used with a switch that could keep up. Protocol overhead with Ethernet/TCP/IP is bad enough without NIC teaming to say nothing of the total throughput of the Thunderbolt transceiver
Why not? A TCP packet is 1500 bytes long, if you are not using jumbo frames, and every packet goes through another interface. You'll need a smart switch for maximum speed, though.