There’s a fairly easy way to test this: use the power telemetry data from the Voyager, Pioneer, Galileo, Cassini, and other spacecraft, which are all essentially powered by nuclear decay. See if the decay rate shows unexpected changes as the vehicles moved further from the Earth.
Great idea for testing this hypothesis!
Someone else pointed out the phenomenon seems to have to do with rate of change in distance — not distance in itself.
There have been several unexpected changes with those flights as Hoagland’s articles on “Von Braun’s 50 Year Old Secret” delineate. See link above.
Interesting idea. However, I think, given the weight penalties and the lack of a demonstrable need to measure decay rates, that the instruments to measure it were probably not included. They may be able to measure the electrical output, but the change in decay rate requires quite a bit more finesse.
A change in the fine structure constant that varied with the distance from the Sun could also explain the Pioneer anomaly.