Yes. Disturbing public life and destroying property should not be tolerated. Especially destroying property. Defeats the purpose of a 'peaceful' protest. The ones would destroy property should be held accountable for their actions. Seems to be pointless to hold protest in a an attempt to hold others accountable for their actions when their own actions arent being checked.
I hate vague laws that are open to interpretation. They are easily abused and can be selectively applied in a way that gives people related to people in power or of wealth special privileges. It can be selectively applied in a racist manner. "Disturbing public life" is a vague, vague statement. Until you specifically define what it is you would count under "disturbing public life" I say "no".
Damaging property on the other hand, that's already illegal. That's called rioting.
Since protesting is legal under the Bill of Rights then I would say that you can't make that illegal. However, rioting is not under the Bill of Rights and is already illegal. So your question is already answered if you bothered to look in to it at all. 50 words!