Answer is it depends. If you have NIC's that support link aggregation (sometimes called Ether Channel or Ether Trunks) and a switch that supports this you can increase the bandwidth to the switch.
Link aggregation drivers usually have several modes- load balancing (no increased throughput), fail-over support (no increased throughput) or ether channel (increased throughput).
Some Cisco switches support up to 8 ports (connections) being trunked. Your limiter here is going to be the PCI bus in your machine- at best you will get 650MB/s through it, realistically only 350-500 MB/s (other system devices want bandwidth too!). With multiple peer PCI buses you can get around this, but you are deep into hardware at this point....