From the bandwidth is is possible to transport the DVI data you described over GigE, since >115MByte/s had been reported and prooved for a particular PHY on the e.g. DE-115 board. But I doubt if it works with a SOPC / Avalon interface. Pure packet writting will be done.
Moreover:I know a project with a streaming interface using Altera's MAC in accordance with an ethernet PHY performing GigE-Vision Standard exceeding 100MB/sec, but it is without SOPC / Nios or any OS.
One system I know is with OS, but does perform more than 400MBit.
A video transport layer in a specialized device for video in surgery field works with compression to make use of around 90MBit, 180MBit and 270Mbit for up to 3 channels of video data.