Have just checked my personaliser. I have no idea if this is new or always been the case but at the top you will probably see: "However, if below your options read ‘Available to book on board’, this means that bookings for speciality restaurants for your cruise are not bookable before your holiday. In this instance, please speak to the teams on board who will advise on the most up to date availability".
Given how "careful" P&O are with words, no I don't think you can make any such assumption. As Moley said earlier, they could be closed, open or fully booked. I for one have had enough and will be moving my very expensive (for me) 1 off cruise to much later. Hopefully by then they will be providing whats in the brochure or at least telling us upfront what they won't be delivering .