Correct. But at least from the switch to the router it'd be fast haha.
Well, probably not. Most cable modems (the router), for example, are fitted with 100 megabit, not gigabit ports, so the switch port with the link to the modem will auto-negotiate to 100Mbps, even though the port may be capable of 1000Mbps. A PC with 1GbE connected to a 1GbE switch will indeed run at one gigabit per second on that link, but the connection to the modem will be a bottleneck. Since the switch will use a store and forward strategy through the speed gearing, no data will be lost, even though you probably don't have flow control engaged. And hopefully any multi-frame messages are sent using TCP, so each connection is acknowledged and flow controlled by TCP up at Layer 4, so you don't permanently lose any of them.