It's completely fine so long as you don't hammer the knife in all the way. Just a few cm or an inch at the most is sufficient, and in my experience that has never caused a problem.
The two main risks with birch tapping are insect infestation and bleeding out from an improperly sealed wound, being the tap itself. I've seen trail crews at my local woodland prune Grey Birch saplings in the spring and then the tree dies a month later. There are also hundreds of diseased birch here, all of which were caused by insects. That's partly why I use a glob of pitch to further seal the tap wound, because it keeps them out...literally using the blood of one tree (adapted to fend-off these little buggers) to save another.