Backend API rate limiting has to surely kick in and force you to wait x amount of time before you try again… Discords bot API actually sends you how long before you retry.
As a client you can hit a server as much and as often as you like. The only thing the server can do is return an error code or try to hold the socket open (which the client can then close on their own).
It can block your IP address at the firewall level. It can't stop you DDoSing it with raw packets, but that's very unlikely to happen unintentionally, because TCP will wait for a SYN-ACK response for at least several seconds and possibly up to several minutes.
