First, let’s look at the circuits involved. The Sriracha is an INVERTING circuit. The Emerald is NON-INVERTING. The Stage 3 is an INVERTING circuit.If you send the signal from the Sriracha through the BnB SEND to the Emerald, the signal returning from the Emerald back to the BnB will still be INVERTED and will blend with the Sriracha to form an INVERTED output. No problem.
Now if you add a Stage 3 between the Sriracha and the BnB, you will change the signal reaching the BnB to a NON-INVERTED signal. This will blend with the Emerald (which will not change the signal) and the result will be a NON-INVERTED output. Again, no problem. As long as your effects are in series, the phase has no affect on the final signal. Phase issues only occur when effects are in parallel. Since the Emerald is a NON-INVERTING effect in the parallel loop, it does not change the phase.
No need for a switch.unless you just want to bypass the Stage 3. Adding a VOL pot to the Stage 3 with a bypass switch will allow you to use the Stage 3 as a level boost for solos.
See the Guides Page section for a thorough discussion on phase relationships.