Games can require a firmware update to play, but AIUI the physical carts are supposed to have their required firmware bundled alongside the game so you can update without an internet connection.
They even did that on the original Xbox. The first year of consoles didn't have Xbox Live and therefore had no knowledge of the service to obtain updates, dashboard updates were delivered on games that used Xbox Live. For that first year, the only thing the Ethernet port was used for was LAN games (and WAN games with private networks). To my knowledge, dashboard updates were only delivered with games but title updates and DLC could be downloaded over the internet.
I'm not positive this is possible. I seem to remember times when trying to play a newer game on the Switch required a system update, even though I had the physical card. I might be misremembering, though.