You can use it without changing
In respect to fast ethernet, STREAMING files isn't an issue over fast ethernet. What is an issue is serving FILES. Getting the files on/off is going to be pretty darned slow and is probably going to be slower than a decent wireless connection is these days.
I would also question if you loaded up the server with 3-4 concurrent streams, even of just 720p, just how well it could handle it. Bandwidth be darned, that is a fair amount of disk hits and caching to manage it all, over a slow connection (which matters because it can't unload a huge wad of data, move to the next request, send huge wad of data, move back. It has to send it in little slow pieces).
Or add in other concurrent work loads, like if you are trying to stream a video to a device, but then go to pull a file or push a file to the server, is it going to be able to handle it between network connection, CPU and RAM without letting the video stream hiccup? I can tell you, I can get my server to hiccup if I try hard enough and it is running a pair of 2TB disks in RAID0, has two gigabit ethernet interfaces, 8GB of RAM and a Ivy based G1620 in it.
It takes some SERIOUS effort to get it to interupt a video stream, but I can accomplish it. I'd think with 1/20th the network connection bandwidth for the server, something like 1/12th the processing power and probably 1/16th to 1/4 the RAM and also probably half the disk performance the threshold to get it to choke like Eddie's dog (from National Lampoon's Christmas vacation) on a turkey bone is going to be much, much, much lower.