Additional features, settings, or issues not covered by specific Microsoft Teams categories
No, the built-in "archive" functionality only works for the Team as a whole. What you can do is enable moderation to prevent new conversations and limit replies to old ones. There is no built-in way to export content from a channel either. You can use the Export APIs to build something around this, though you need to meet some requirements first.
Some third party products offer an "archive" feature for channels in terms of copying content to a different ("archive") Team and scrapping the original channel, but this is more of a workaround/hack with some limitations (i.e. you will lose the original timestamps).