Possibly? The paper isn’t really clear enough for me to figure that out.The intro text says
Consequently, any discrepancy between the data averaged posterior (1) and the prior
distribution indicates some error in the Bayesian analysis.
and Theorem 1 says
\pi(θ | \tilde{y}) for any joint distribution \pi(y, θ)
but it’s not explicitly stated it should work for any arbitrary prior so I’m not sure.
Agreed regarding checking out the traces as a useful tool. It can help make sure your method is sampling properly, though you can’t tell from looking a single trace if the method is properly calibrated.