Obsidian Ant and others have observed they will likely be persistent because other players can dock at them. Since they are not pilotable and will be stationary, this makes sense. Otherwise...you log off and then what? People already logged off on your carrier just 'disappear' and 'reappear' in normal space?
As for destructible...meh, I get why it is a request but I don't think these personal carriers are the right way to go about that. More importantly, I don't think that's Frontier's style to be honest. If you want ruthless gameplay (nothing wrong with it, by the by) I'm not sure Elite is the right game for it. EVE Online is great for that and built from the ground up to support it.
It also has less than a hundred thousand subscribers. 'Hardcore realism' just doesn't sell very well.
Gee, I wonder why.