if you ping a consistent 3000 and send a packet every 1000ms, you are still telling the server every 1000ms that you want to perform an action. it's just 3 seconds delayed
the server still receives your packets every 1000ms and performs the corresponding action (though it doesn't show on your own screen for another 1.5 seconds, the time it takes for the response packet to be sent to you)when you have to deal with lag every day you kind of figure these things out...