Depends. You aren't out anything by trying.

I always try it when flying WN and if DL uses the same TSA entrance I have always been able to get through by flashing my PM card with no problem. (DEN, MDW, BNA). In fact at MDW it says on the sign who can use the priority lane it mentions Delta Medallians (doesn't say SP or Gold or higher like other airports) and doesn't say you must be flying that airline.

At airports where DL is out of another terminal usually doesn't work, but has a couple times, so just try it but make sure to allow enough time to go through the regular line (which can be long and makes you appreciate the SP line at certain times). At LAX and LAS I have never had any luck. SFO it worked once and was denyed the other time. At DTW I typically get denyed but once they waived me right through and another time I thought I was going to be denyed when she asked to see my boarding pass and then she said "You are a southwest RR member so you can use the lane (even though I am kettle status with WN". What really iritated me when I was denyed at DTW was the week before the one time I was denyed I was on Delta and some flashed a WN A-list card and was allowed in the SP line at DTW.

I am glad to hear they are enforcing SP at DTW. When the downstairs SP lane was there, the majority of the time the screener wouldn't check the boarding pass. It will be worth hiking upstairs if they are enforcing the SP lane now.