I doubt that, as the browser add-on is a standalone product as far as I can see, and there's nothing on its download page to say it only works properly if the main Avast program is installed.
In fact, one of its settings "Secure Browser" does say it only works if the main program is installed, but no mention on the others.
I'm wondering if your popup and mine are actually different things.
Mine says "This site could have harmed your computer", which is a bit strange because I thought it was supposed to warn you
before any damage was done, not afterwards!

I don't speak German, but I think yours is just a warning about phishing.
Maybe one can be overridden and not the other.
