yes it can

Powered monitors have a line level input and then add current and perhaps a little gain to the speaker drivers.

Is this radio station getting into the speakers even when the mixing desk is not connected ?

If you have XL inputs on both speakers and mixing desk then use a balanced shielded cable.

If all you have is RCA's then use a sheilded RCA to RCA cable.

A simple speaker style Fig 8 cable is not what you want here.

hope that helps a little

this one is a tough nut to crack. I would start at the beginning of your signal chain (where the signal levels are the lowest) and try to isolate the noises there. mic cables, bad (dirty) connections, poorly-grounded, ungrounded, and/or shielded electronics, bad (intermittent) cables.

I have a 17.5 KW FM transmitter whose antenna is ~750 feet from my studio . All our studios (including our performance/recording space) are totally enclosed with copper mesh screen. Without it, RFI gets into everything.

Also, some equipment just won't work in high RF fields. And, the more balanced I/Os you use, the less noise you'll have.

It's detective work - good luck!