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.
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.
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.