Capt C.
If those other devices are powered off when it happens, the answer is no.
If the problem only happens when those other devices are on, it could be either or both causing it, I suspect the device you turn on causing it.
Either borrow a VHF radio or GPS, or go to flea market and get $7 dollar used car radio and hook it up, see what happens. Use process of elimination, act like a detective, this isn't high tech.
Alternately, you can remove the GPS or VHF radio and walk it over to a buddy's or slip neighor's boat and hold it near sterio, make up a fused clip lead feed to connect to the battery.
There are much more expensive ways to figure it out, like wholesale replacing units until you hit it, called the shotgun method used heavily in the auto industry, I proposed cheap way to get it done, only time involved and a few favors.
Your boat's grounding system may as well to fault too.
If you can get a good honest electrical guy come down, who you make sure knows you are on a budget (even if not), he will figure it out lickety split. Has to be good and honest, good luck !