If you mean you want to be able to max GigE from the server on one client, while streaming videos to another client, then yeah what I described should work fine provided you have the IO bandwidth to back it up (trying to copy huge files at high speed while streaming something else tends to kill performance of mechanical drives, so it might be worth experimenting with a different volume for media, or some sort of caching).
Or, as shaithis says, you can do link aggregation at higher layers provided both ends are fully aware of it. If all you need is access to the filesystem, then an iSCSI volume might be a good idea, but it's treated more like a local drive, with the client handling the filesystem etc, and only one client can use it at a time.
You could get something like this http://www.amazon.co.uk/dp/B000RAILSQ but with two two-way LAGG groups, you've already used half of the ports.