If your computer has a 10gigabit NIC and the router and destination computer have a 10gb NIC, then you could theoretically get 10gb transfers within your network if the drives on both ends could sustain it.
Most HDDs top out around 150MB/s reads and usually noticeably slower writes, so no in that case you wouldn't be able to take advantage of much more than gigabit speeds (1gbps/125MB/s).