She wants to know if it's a good idea to send a quick note of thanks and acknowledgement to new subscribers. Cat says, “That was my first instinct, but then I wasn't sure if it would be appreciated or invading their privacy.”
I suppose it's possible that some people would prefer to subscribe anonymously, but everyone should understand it is your blog and that you have access to their subscription.
Most people will be blown away that you took the time to personally acknowledge their automated subscription. I say Yes! Do it! Send a personal Thank You to their inbox and turn them into a fan for life.
Don't be wordy. Don't copy and paste the same text over and over again. Just say Thank You with sincerity.
Address the person by name if you have a name and be sure to sign your full name to the note.