Does an engine management light fail an MOT?

Yes. The engine management light is specifically checked as part of the MOT's emissions section. If it's on when it shouldn't be, showing that the engine management system has spotted an active fault, that's a genuine MOT failure item, not just an advisory.

This is different from a light that briefly comes on during start-up as a normal bulb check and then goes out - that's expected and not a fault. It's a light that stays on, or comes on and remains on, that causes a problem.

Source: gov.uk: car parts checked at an MOT