English equivalent of Polish saying "You let a boor into office and he will drink ink"

One of the closest idioms to this I know of is like a bull in a china shop meaning

very ​careless in the way that they ​move or ​behave:

Or alternatively, fools rush in (where angels fear to tread) which means

"The rash or inexperienced will attempt things that wiser people are more cautious of."

The [Yale] Dictionary of Modern Proverbs (2012) has this possibly relevant saying:

You can put lipstick on a pig but it's still a pig ([or] A pig wearing lipstick is still a pig).

Wolfgang Mieder, "Yes We Can": Barack Obama's Proverbial Rhetoric (2009) offers a series of closely related sayings:

From the twentieth century there are also such variants [of "lipstick on a pig"] as "A pig in a palace is still a pig," "A pig with feathers behind its ears is still a pig," "The pig may have a tuxedo on, but he is still a pig," "A pig painted gold is still a pig," and "A pig in a parlor is still a pig."

The point of these expressions is that putting something (or someone) in a setting where it doesn't belong won't change the thing's nature, and may have harmful effects on its new environment.

Hanging oneself seems pretty idiotic, so “Give someone enough rope and he'll hang himself” might capture the meaning of the Polish saying in certain contexts.

Prov[erb]
If you give someone that you suspect of bad behavior the freedom to behave badly, eventually he or she will be caught and punished.
Jill: I think Matilda's been stealing things out of my desk. Should I tell the boss?
Jane: No; give her enough rope and she'll hang herself. One of these days she'll steal something important, the boss will find out for himself, and he'll fire her.

(from ‘McGraw-Hill Dictionary of American Idioms and Phrasal Verbs’ via ‘The Free Dictionary by Farlex’)

Sounds like an accident waiting to happen.

2 A person certain to cause trouble.

http://www.oxforddictionaries.com/us/definition/american_english/an-accident-waiting-to-happen