Depends entirely where you were in comparison to the servers. But it wouldn't take any time if you split up the site into a few different servers. One for MySQL, one for images, one for the actual php pages (even though all this is overkill) we would also assume that all these servers all have equally ridiculously fast connection speeds so there should be no delay since you are simply loading one thing from each identical server.
Technically it should be faster then running everything on one server because if a single server had to do all three it would have a small amount of load where as if it were separated there wouldn't be any load at all. There would be a small delay between the php file server to connect to the mysql server, but since datacenter connections between each other are ridiculously fast you wouldn't notice it. But maybe you are right, that small delay may cause it to be slower then a single server.
Now if you were to take one 100mb sql database and distribute it between 10 servers, you would be right elight, there would be a delay.
But having a seperate server for images will increase speeds (maybe even one for dns hosting, and maybe one more for cdn hosting, and one for mail hosting.. lol)