Closing a partition is good, but you should not mark the disk as Read Only. A closed partition, as already said, is not actually ignored. It is referenced by processes that include Storage Expiry, User Deletions, Sharer Info updates etc etc.
A monthly backup for this should be ok, depending on your storage expiry times and the amount of data you are archiving etc etc. The main thing to remember is the databases will be changing every day, and if you did have to restore to a previous time, you will at least "hopefully" have more data than you need in the closed partitions, as the DB will probably have removed references to it.