Why it is a question
Sefidgaran and Zaidi (LIT-233) build their variable-size codes only for finite alphabets (Theorem 2). Their general Theorems 3–5 are change of measure plus Donsker–Varadhan, to which they give a compression reading (NOTE-806). The audit’s re-derivation of THEORY-263 shows that, with the rate set to the pointwise information density against a fixed prior, Theorem 1’s bound follows from the disintegrated change of measure and a subgaussian moment bound, in any measurable space. So in general spaces the bound does not need the covering. Whether compression is nevertheless the mechanism, in the sense that a covering construction exists there and yields the same or a tighter bound, is open.
What would answer it
A source that builds a variable-rate covering for continuous outputs and derives a PAC-Bayes bound from it, with constants matching or improving the change-of-measure bound, would answer it yes. A proof that no such covering can match the change-of-measure bound outside finite alphabets would answer it no. Whether either bound is tight or non-vacuous for networks does not settle it.