I have had no problem with priority check-in and boarding. Indeed with DL, you won't be Skypriority but with Zone 1.
Usually the signs at check-in/boarding say:
Skypriority passengers
We also welcome Skyteam Elite
Some airlines DO have seperate counters for Skyteam Elite and Skypriority.
You certainly have priority during your trip, Skyteam Elite beats *A big time.