Changing the question just slightly...
I know that IP hash based teaming will give us the 3GBps aggregate bandwidth if I have dozens/hundreds of hosts hitting the server/VM. But, let's say that we are doing a file copy/backup between a VM on one server and a VM on another server. IP hash based teaming will only provide us with 1Gbps between the two VMs. I don't see a way around this, no matter how many NICs and vNIcs are in play.
Is there any way; using some other networking configuration, specialized copy/backup software, IP addressing/routing tricks to make the backup actually utilize the 3Gbps potential? It seems that it should be possible, but I don't see any way to get away from VM host to VM host, on another virtual server, going through one and only one physical NIC.
Now, returning to the original poster's question...
You may wish to consider 10Gbps NICs, at least in your VMware server(s) and your backup machine. A directly cabled link between the two machines will afford you lots of bandwidth for your backups without having to spend really big money on a 10Gbps switch.