They do, but more importantly, they vary between Accor-managed and franchise properties. The level of security when booking a non-prepaid rate is minimal when it comes to franchise hotels (in Europe, at least), and even some Accor-managed hotels where, as you said, it all depends on the level of security employed by the management. In essence, somebody often has to key in the number of a screen (or, even worse, a print-out - I've had this multiple times when my CC details where appended to a booking waiting in an envelope with my name on it for the agent to key in) into the terminal to remotely charge the card.

All in all - there is a way to see your CC details when you book a non-prepaid rate, which, in this day and age, I find quite disastrous. But then again, knowing Accor's IT, it is still better than being randomly charged by a moody system...