On the evaluation board, yes. This board is not optimized for high readout rate. If you do your own electronics, like GBit Ethernet, you could be much faster.
What is the readout rate via GBit Ethernet that you have achieved?
Where is the bottleneck in ethernet?
What is the proposed scheme by which the GBit Ethernet will be implemented, will the DRS4 Eval Board have to wait for the computer to respond before sending the data (wouldn't this make the readout much slower?), or will the DRS4 Eval Board keep sending the data to the computer?