If it contributes to you're peace of mind, OK, but I'm not seeing how a camera as described is really going to do anything material for you. Perhaps if there's a conspicuous security camera it might serve as a deterrence, but after the fact it's not going to do much, unless it's someone recognizable to you, like one of your neighbors or something. It's way better to put effort/expense into not getting it stolen in the first place than trying to recover it after it is.

If you must keep the bike in the garage and the garage door open perhaps you can arrange it so that the bike is out of sight from passers by. A decent lock would also be a very good idea. My garage doors are on the side of the house and the house is on a hill set back a good distance from the road so it's not possible to see into the garage from the road. Even with that, I keep the best bikes in the house rather than the garage, and keep the garage door closed most of the time anyway.