Can an email be sent in Appian for user creation and user updates, if yes how?

when you use admin console to create the user, you shall not be able to do so as far as I know. But you can do few things 
Option 1. Develop a process which creates the user and also inform admin team
Option 2 Get SSO enabled on your Appian instance so that users access is controlled centrally 
Option 3 run a process periodically so that it picks up all the newly created users by checking "USER" record and user function 

YOu can develop a process that is started when an email is received and creates or updates the user ....

https://docs.appian.com/suite/help/23.1/Sending_an_Email_Message_to_a_Process.html

So, that user creation or update must be triggered by something. In well managed environments, I see the following options

- Single-Sign-On with an external identity management system

- API calls coming from an external system

- Processes implemented in Appian

No option is, to allow user creation from the admin console.

The first option is completely outside of the Appian scope and any requirement must be implemented there.

Second and third option involve an Appian process and you can do whatever you need/want to.

So, can you describe the actual requirement in more detail? And what makes "the right solution" for you?

You could have a process monitor the user_management.csv log and send an email whenever it detects a user create event.