If they were done live, it presumably wouldn't be by getting the prop phone to ring, it would be played in as an effect
I was thinking they'd want to do it live so it sounded realistic - for example in the episode it rang in his pocket, then he brought it out to answer it. But it's probably much easier to add it in post with a filter.
I still remember being impressed by an episode of Eastenders where a plane was heard going overhead (wonder if they still do that, haven't noticed) outside, and could be still be heard when the scene cut to inside. Ironically I was doing a sponsored silence at the time, but forgot, and remarked on it.