@Mountain Pond Apologies for the delay in reverting back on this, as I was checking with my team on your requirement, below is the update I have,
No, this is not possible currently, What you can do is to configure a notification rule to send an email when there are certain exploit or vulnerability events, such as a new public exploit, but you cannot do this for all/new security recommendations.
If this is a feature you are looking for, please utilize the feedback button in the portal or post your feedback on https://feedback.azure.com
Let me know if you have any further questions, feel free to post back.
Please remember to "Accept Answer" if answer helped, so that others in the community facing similar issues can easily find the solution.