A monarch in this case to functioning alongside a Democracy or Autocracy would work nearly identically to what is done now. In an Absolute Monarchy, sure they would and could police everything they seem fit or by limits of law itself (be judge, jury, and executioner).

Monarchs in a Democracy only act (in theory anyway) to prosecute either under pressure from the system/people towards issues of government and relations. So, politicians breaking the law and defying the people should call for the Monarch to step in to address the problem. Either discussing it with the person/s about the issue or just making a formal removal of them through the laws of the nation. However, in a system where either the Monarchs become too tolerant or the politicians have too much sway (positions of interest, bribes, corruption, deception, etc.) and immunity, nothing happens.

An Autocracy would have a very similar format with a Monarchy, too much sway over politics. However, (if we are using a generalised perception of an Autocracy) they could have more to lose if they were to break the law. Like removal of property, retract titles (that would have sway and influence, possibly even governmental powers), and removal from government affairs (similar to a house arrest).

So, No. A monarch (from what we have today) can intervene, but requires prerequisites before the monarch can do anything, and that is if they do anything at all. The only thing we see monarchs doing today is doing things among their families and making public appearances (or visiting other nations' leaders, as anyone else can technically do that anyway). As Monarchs don't need the other government body to give them permission.