Dan, I have three points.
1. Some DI papers don't respond to carbonate solutions, only hydroxide solutions. This is due to the weak nature of some of the incorporated developers or their solubility in alkali.
2. Ilford MGIV paper, a paper that we all probably use, fails a test with NaOH turning dark grey at the maxiumum exposure. It might fail your test, but it is a DI paper.
3. Even passing the test you describe does not mean that the incorporated developer is not present or not active in the carbonate solution. It may cross oxidize with normal developing agents in solution and thereby become what we call an 'eta' (electron transfer agent). Failing the test does not mean that the developing agent plays a significant part in imaging either. It may just accelerate normal development or tweak curve shape.
PE