"Does the radio explode?"
터져요 is more like a slang which means if the radio gets frequencies and signals...but of course, this kind of lesson shouldn't be here
라디오가 터져요? is a fixed expression which means "Does the radio work?" or "Is the radio working?" in English
My wife is a native speaker.. and said that this expression is used to say that the radio has a signal
What you mean can be like this: 라디오 방송이 잘 터져요? or 라디오 방송이 잘 잡혀요?
"TV/라디오 방송이 잘 터지다" can be understood, and there are some people who say like that. But that has some sense of slang. '라디오 방송이 잘 잡히다.' or '라디오가 잘 잡히다' is the most neutral and favorable expression.
Just saying "라디오가 터져요?" is almost always understood as "Is the radio exploding?" .
With adverbs such as '잘'(well)' and '안(not)' the sentence can can be understood as both meaning.
"라디오가 잘/안 터져요?"
However, remember: using'터지다' as a verb meaning 'work' or 'function' give some feeling of slang, and is not recommended.