While long time EXP, and AC Card Member, my company negiated some number of deals for execs to get all 3 (EXP, AC Card and Concierge Key). EXP is a wash for me, already have it. AC was nice, as I didn't have to pay for the year. But Concierge Key can be amazing!
On a connecting flight from AA to BA in LHR, they met me at the plane and drove me over to T5. Cool. The rest was on my own, they did not have me cut any lines.
Most recent, flying through SJU with family and lots of dive bags. She meets me off the plane, escorts me to "crew" lines for Immigration, helps me get my checked bags, gets me through "Crew" line for customs and takes us to the head of security line for reentering the aiport. She escorts us to the AC, and tells she will come get us when ready. She walks us over, boards us first, says have a nice day. Wow. My son was blown away.
OTOH - went through Dallas a couple of weeks ago, nothing special there. I think it is done on an "as can" basis.
When it works - it is terrific.