When a critical log is catched you do get an error if your application runs in the cloud portal. It will not send you mail for log errors you place yourself in the log. If you want some notification on errors you want to know about create your own mail routine or make a scheduled event routine that retrieves all your custom made logs messages and mail those to the app admin.
If you have the logging module in you app, logging is persisted to a database object. You can easily create a microflow to send an email, after a logging message occurs with loglevel 'critical.
Be aware, that after a critical log message, it could be that sending an email isn't possible. Something went wrong and some functions may not work in your app.
We have implemented such a module but is not yet in the Appstore. Send me a mail, I'll send you the draft module