With LDPs, you'll easily pass the OBD "Readiness" check, which is what the Emissions Test queries the ECM for.
The secondary cats are solely incorporated by the auto manufacturers to prevent cold start emissions. Until the primary cat "lights off", and the ECM goes into "closed loop", the "open loop" (w/o the primary O2 feedback) emissions are controlled by the secondary cat. Once the primary cat "lights off"/is activated, the secondary cat is basically along for the ride.
All state emissions checks are performed with cars in "closed loop". Therefore, the secondary catalytic converter does not factor into the OBD "Readiness" check. Unless the Emission Testing Station includes a physical check of the emissions equipment, having LDPs installed will not raise any queries.
As for Full Catless DPs not causing a Check Engine Light (CEL), that's fine, however, the Carbon Monoxide smell will certainly result in further scrutiny by the Emission Station Inspector(s), because your exhaust will stink!