Does it help to climb in case of a partial engine failure?
Agreeing with @Antzi, high engine speed when combined with some sort of small scale physical damage or corrosion is a typical failure mode for propeller engines. Combining that logic with the fact that propeller engines run more efficiently at lower elevations (higher air density) I would recommend against climbing. In fact, lowering your elevation and speed will greatly reduce the stress/strain you are putting on the engine and will likely give you a better chance of making it safely to the closest airfield.