Possibly but there are other things that come to mind that may be able to cause the same problem. I have a Taurus and it leaves the window toggle lights on for five minutes after I turn it off, however it's designed to do that. It does cut off the radio though. There may be a way to make it do what it's currently doing in the owners manual. Although my car doesn't have that option, it has a lot of other ones.
I would bet the radio and other things being on are controlled by a relay either in the dash or in the engine compartment. Check your owners manual to see if there's one that controls the radio, power outlet or other accessories. Did this start suddenly, or has this truck always done this? A previous owner could have done a custom wiring job to make the radio stay on.
Last I'd check to make sure the key is actually in the off position, rather than the 'access' position that will leave your radio on when you remove the key. The access position in many cars is further back than the off position. Of course if it allows you to remove the key when in that spot then there is something wrong with the ignition switch, because they're designed to not release the key in that spot. One last point I'll make is if the ignition switch is faulty it's likely that wiggling it with the key in or out may cause the radio to turn off sometimes.
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