Something that has not been really touched on during this discourse is that if you are on an AA flight, no matter who is flying it, if you are a D1 or D2, you are just like any other employee using their travel privileges. Other airline, or other airline flying on Envoy/AA is using reciprocal JS agreement. These really are two different things. We may end up on the JS and use that ability because it is full in the back. If so, then regular JS etiquette applies. Is it courteous to check in if you are a D1/D2 and have a seat in the back, sure, but not required.
The OP was about an Envoy on Spirit, but there are lines that have been blurred in this discussion.
All that being said, I still agree that you must be properly dressed, etc. either way and when required, check in and ask for the ride.