Tested this now. I created a new topic under Shared Drafts with an AP-enabled tag:
I am not getting the Invalid date issue, however, the post shouldn’t be marked as published. In fact, publishing shouldn’t start at all, this is a topic in a private category. Just saw it published to https://socialhub.activitypub.rocks/t/testing-a-shared-drafts-issue-with-activitypub/5079.