This is probably a complete waste of time since none of the recent suggestions have had staff replies, which I find disappointing and would put me off of purchasing or donating anything to CSF...
Anyway, I have just set WHM to email me with alerts, and decided to add Pushbullet for more severe alerts. I thought it wasn't working when I didn't get login alerts but realised this is from CSF. I tried a cPanel alert like a backup success and it worked. On investigation I found that CSF emails the root user. Although the email address can be changed in CSF on a per-alert entry, or cPanel wide via "Edit System Mail Preferences" which forwards root emails to your chosen account, there is currently no integration with cPanel's contact manager meaning any CSF Alerts aren't sent via the other ways I have set up, in this case, Pushbullet.
I would love to see CSF integrate some way with it so that I can choose to have CSF alerts be pushed to Pushbullet or any other contact information set up within the cPanel/WHM settings.