Doubt that. They care about average call metrics but not why people are calling, and the call center operators have absolutely no ability to fix anything and will just work to get you off the call as quickly as possible.
Doubt all you like. Customer support is a huge O&M cost to these companies and they will do nearly anything to reduce calls. I know they track why people are calling, or at least my place does. Half of my career has been spent writing software and making changes to our websites to reduce call volume.