Depending on your encoding method (which will determine your hypothetical maximum bandwidth to begin with) the two computers will establish a connection that will give them a rough estimate of transfer speed based on the packet rate. In my experience in video sharing sites, the issue was best mitigated by several smaller "fast" servers acting as the fetch and delivery machines, while other machines packed with disk drives handled the actual storage of the media. Those "fast" servers were generally at the mercy of the internet connection, both at the data center and all the way to the end user's location.
So the short answer is yes, the better/faster the delivery hardware is, the better a video stream is going to perform assuming the connection to the end user is okay.
