Assuming you mean "server" as in a dedicated server (i.e. not the internal server running when you play singleplayer), I don't think so. You would likely see block update lag and similar, but not FPS drops. Case in point: when the server goes down completely, you can sometimes still move around flawlessly for a minute or so. Your client can replicate your movement, collision, etc. without a connection to a server for a while. Only when the client is definitely sure the server is "dead" it will drop your connection.