The body doesn't just use carbs because they are a cheap or easy energy source, it uses them because certain energy systems require them to be used.

Anaerobic activitys need Carbs for muscle contractions to happen, Aerobic activtys can run off fat or carbs.

But boxing is mainly an Anaerobic sport (esspecially amatuer boxing) which makes it stupid to have a low amount of carbs in your system.

You might start to burn fat for a long distance run insead of carbs but bag work, sprinting, Plyometrics, Calisthetics?... you barely use any fat for energy in those activitys.

You will train like piss.