Yes, it is possible and it happened to several websites. Google does not send a message about every single google penalty. Here are some examples when Google does not issue an error message in the google search console.
Mixed content errors:
When the hostpage protocole is HTTPS and when the links on this page are in HTTP, we don’t see any errors in the Google Search console.
Redirection issues:
Sometimes when webpages don’t contain a canonical URL. Google may not really know what should be the URL of your page if several URLs display the same content. Google didn’t say it was a google penalty but we consider it to be a penalty.
Titles contain long numbers:
Once one of our websites have been penalized by google because there were phone numbers in the titles. However, there were not notifications in Google search console.
Conclusion:
It is advised to investigate and read articles about penalties and SEO to understand why your website traffic has dropped. Don’t only rely on the google search console.