Does rebuilding a clustered index offline require extra space for each non-clustered index?

nope

Rebuilding the clustered index will not rebuild nonclustered indexes unless you're changing the clustered index key columns.

You would also need to rebuild nonclustered indexes if you were adding a clustered index to a heap table, or dropping the clustered index, to swap keys/RIDs in the nonclustered indexes depending on the scenario.

Clustered and nonclustered indexes are separate objects, but in SQL Server they are related. Nonclustered indexes inherit clustered index key columns in order to facilitate lookups, etc. That's why some clustered index changes will necessitate nonclustered index rebuilds as well.

If you want to do this without the user database growing, it may help to add the SORT_IN_TEMPDB option to your index rebuild command. That way you only need to worry about the filegroup your index will be created on having space for the new index, rather than the new index plus the intermediate sort. This may grow tempdb, depending on its current configuration.

If that's a problem, you can restart SQL Server afterwards to set tempdb back to its default file sizes. Since you're able to rebuild a ~66GB clustered index offline, I'm working under the assumption that either this is not a highly sensitive 24x7 workload, or that this is a non-essential table.