Thinking"out loud" here ...
This is difficult for a few reasons. We rebuild all test connections every night. This means that all test connections are "new" every day.
Test connections change because family connections are added and edited. That is, it's not just that new tests are being added. Tests are connecting to different profiles based on the family relationships of the test-taker.
We would need some system for tracking when they're "new."
Who would the e-mail go to? Probably the profile manager(s), not everyone on the profile's Trusted List. Though, if it were in the weekly Activity Feed update that wouldn't be a burden.