Is it possible to pick up radio interference over your computer's speakers?

Yes, it is possible. The wire of your speaker acts as the antenna, with the magnetic in your speaker, power with antenna. If the length of the wire matches the radio wave length, speaker picks up the frequency and acts as radio.

Speakers by themselves aren't able to receive radio signals, so I don't know what's going on. Are you maybe hearing someone else's radio next door?

no and it shouldnt to get radio interference you also have to be on some kind of radio. it may have been a popup. sometimes when they come up they start talking.

Hahaha.

If they're wireless, yes, it's possible.

If they're wired, it's most likely an adware or spyware on the computer, that has volume. Or, it could be an ad in general.

Yes, if you have wireless system it can happen. I had it happen once with a wire system. Very rare

i get radio in my guitar pickups..they are active electronic.. also in my effects.... i don't know why.. somehow they just pick up the frequency

yup. mine does