For phones & such, it might be ok. It's really the phone that "goes off" . Try my battery is about to; go flat die fail give up give out fade my battery is; nearly depleted nearly flat

No, that wouldn't work. The commonest phrasal verb here would be 'run out' (as in 'run out of charge'). If something runs out (money, for example), you have used it all and there is none left. 'My battery is about to run out'. 'Go off' can mean various things depending on context. For example, 'My alarm went off at 6am' (meaning 'ring'). Another meaning, especially in BrE, is to become stale, for example 'The milk will go off if you don't put it in the fridge.'