They do monitor it. They don’t block IP addresses though because anyone can change that in seconds. They are not permanent.
To explain a bit more about the account security. Blizzard does pay attention to login patterns and locations. If you DON’T have an Auth on the account it is very sensitive to changes and will lock the account pending password change when it detects something odd. Having an Auth on the account reduces the chances of lockout because you have the Auth to stop them - and to prove you are you.
Why not lock the account even with an Auth? Because people travel for work and it would lock you out just going to the next state or getting a new PC. The Auth reduces that annoyance.
If you are getting attempts at logins then someone has your email for the account, password, and possible access to your email account.
I would first scan for malware on your PC. When clean, set up an email you use only for your Bnet account using a service that has secondary authentication. I use gmail. Change your Bnet email to that new one. That email address never gets used elsewhere so can’t be stolen. People can’t get into it because you have secondary Auth on it too.
That should stop any attempts at logins unless there is still malware on your PC.