Yes and no.
The CSV files are mainly for account transfers, but that does require both servers to be active at the time of the transfer.
There's also a different system which is your account archive. You can get this by clicking the "Request your archive" button below the CSV list, on the "Export" page.
This does more than the CSVs, it downloads all your posts etc.
Mastodon doesn't (currently?) let you upload this to a new account, but another Fedi platform Firefish does.