My advice to you is if you haven't already bought into the policy , wait until your VRD arrives just so that you'd be on the safe side.
If you don't have the correct paperwork on the installation day then the CO-Op can be funny about it and without warning threaten to terminate your insurance, its happened to a few people I know.
I waited until I had all my correct documentation before I bought into the insurance m saying that it only took a week from me sending it to their office for it to arrive back to me, it could be a week, a month, 3 months, you just don't know, it also depends on how busy they are and how many have been sent in I suppose
EDIT: If you don't have your logbook when the box installation man arrives , you will not be charged so long as you can show him your driving license and the named if one is added, it will still be required though within 45 days of the commence date.
If you are unable to provide him with your license and the named license then your installation will not proceed, you will be charged I think £45 and another appointment will have to be made, the box must be fitted within i think 24 days of cover starting or else I believe the policy will be ended, hope this helps