Can’t answer yes or no. The answer changes based on carrier.
It was already answered in that post and the follow-up post from the developers. The answer is sometimes.
They do not contact ISPs when a player has a connection problem, so it doesn’t seem likely they would reach out to a mobile carrier. In both cases, Blizzard is not the customer of those companies.
I do not work at Blizzard. I have linked the information available on this topic. If you want to discuss the issue further, please open a ticket with Blizzard Customer Support.