It should work right away if they've already authorized the terminal. I also assume you've requested the HD service to go with the terminal, and that SHOULD be available as soon as the box is working. This is, however, Rogers, so you're mileage may vary.
Once you have the STB connected at home, it should only take minutes to get it authorized - you'll need to call Rogers to get that done - there's a special number that comes up when you plug in the terminal. I don't think it gets activated before then.
If you have filters for some of the analogue channels, then they will need to be removed separately if you have some TVs with analogue tuners where you may want to get more channels. That is up to you obviously - whether you wish to go for more than the basic channels. Just as an FYI, here's Rogers HD Offering:
To provide "basic cable analog service", which in most cases is 2-28, the cable company installs an RF filter, usually in the CSE (Customer Service Enclosure) on the side of your house.
In most cases, the filter is designed to allow the channels in which digital signals reside to pass through. Depending on your location, there may be some exceptions. If you're missing anything on the digital side, it may be necessary for Rogers to schedule a technician to remove the filter.