He’s specifically asking about connecting to the garage door, not any point of the house. This should be acceptable, with a door/gate entrance/exit of course.
The proper legal restriction of a driveway is much debated. I would leave it implicit first, and only put access=private on the gate/door.
I wish there were a way to up vote answers on this forum as I’d up vote this one.
Especially the part about legal restriction of a driveway. That varies quite a bit based on where you are. My sense of the fairly recent discussion on this on the tagging email list (or maybe it was talk-us) is that if you feel you really must put an access tag on a driveway to a house it probably ought to be
access=destination
unless there is a gate or visible no trespassing signs on the ground in which case
access=private
could be okay. But since the situation is usually not visible in aerial imagery and since local laws vary, it is usually best to simply leave the access tag off and let the local convention, what ever that is, be assumed.