Is it possible to programmatically mark all posts on a board prior to a defined date as read-only?

Yes, that should work, You can update the "read_only" field to "true" via a API v2 call on the messages collection:

https://community.lithium.com/t5/Developer-Documentation/bd-p/dev-doc-portal?section=commv2&collection=messages

If you loop through all the non-locked topics before the given date...