The same thing would have happened because it's not for House officials, the Clerk, or the Speaker to make a decision regarding the House's privilege. It's only for the House itself. It made things more difficult in the summer, in August, when only a few of us were in the office and no members were sitting.
If the House had been sitting, I think maybe consultations would have taken place earlier, more easily. But I suspect that, based on the fact that this was the first time we were in the position of applying the privilege to specific documents, the process would have been the same.