This might be a weird question. Is it possible to connect a FreeNAS server to a computer with USB 3 and use the NAS as a high-throughput external drive? We would want this sometimes to not be capped by the GB ethernet limit.
Not really, no. USB3 is only 5Gb, you might consider adding 10GbE if you need the speed.
Also, you should be able to squeeze 100MBps out of 1GbE. Make sure you're getting that before considering it the issue (I see people running FreeNAS on ancient hardware sometimes).