What is the rational significance (significance in the context of rationality) of a belief being rational or irrational if it has no correlation with rational or irrational outcomes? [I really should qualify here that I am referring to some kind of theism which is consistent with, though not supported by, all empirical evidence.]

I'm not sure what you mean by rational or irrational outcomes; there are only outcomes that a belief predicts. If a belief predicts results identical to its own negation (that is, does not correlate with results at all), it is useless and can be safely culled by Occam's Razor.

Also, the only theistic hypotheses thus far that have not produced poorer results than some non-theistic hypothesis are ones positing supernatural entities that either do not interact measurably with the universe or do so only in ways indistinguishable from random chance, neither of which is a particularly common idea among actual theists, so it's something of a distraction to limit ourselves only to theistic beliefs that are not reflective of a typical theist.