Does GMAT prep transfer to GRE prep (or vice versa)?

There's significant overlap. Both tests cover algebra, arithmetic, data interpretation, and reading comprehension. If you've prepped for the GMAT, much of that math and verbal work carries over to the GRE. The main differences you'd need to address are geometry (on the GRE, not the GMAT), GRE vocabulary, and learning the Quantitative Comparison question type.