Might work, but that's a very high-stakes maneuver that could backfire possibly even worse than through HR because now you have two people with the power to make your life hell and potentially no record in HR about the situation (potentially losing first strike opportunities - now your manager or manager's manager can begin to record problems caused by you before you can record problems by them). And also IME it is basically impossible to read how your manager's manager feels about your manager

Realistically if you have a bad manager your only 100% safe option is to switch companies. Switching teams internally can work depending on the place, but it does carry risk, especially if you're on a visa