>And would it work on my bedside clock-radio?
Depends on the radio. We've got a couple of Squeezebox radios, They look and work a bit like an old fashioned radio but they're Internet radios. They're also quite old which means that they've missed out on the relentless improvements (i.e. integration with remote site all the better to monetize your use of the thing) have passed it by. (The audio quality's pretty good as well.)
(Then there's always Alexa, everyone's best friend. She turns up in all sorts of things, including something that looks like an old fashioned digital alarm clock. She knows about podcasts.....)