I tested network throughput with
iperf and it can push around 90 Mbps of TCP through happily. If I recall corectly, Full HD video requires around 25-35 Mbps, so my guess would be that yes.
You may want to consider something faster than a SD card to store media files on. While a Class 6 is probably enough, Class 4 probably isn't.
I did a more realistic test of I/O - reading from SD card and pushing the data over the network.
On Raspberry Pi (Raspbian):
nc 192.168.105.225 337 < /dev/mmcblk0
On another machine on the same LAN (bridged):
nc -l 337 > /dev/null
The router (bridge) showed 44 Mbps of traffic being pushed by Pi. Considering that I have a Class 4 SD card this implies that I/O on Pi is not a bottleneck at these speeds.
Resource consumption during a test (it's quite high):
I will try with an attached USB hard drive soon to see if it can push a full 100 Mbps.