I've been able to get a specific car for a mini-lease multiple times at a major international airport location. They can pull a vehicle and hold it for you in the lot. But at a big airport location, even that isn't foolproof, as another agent may just rent it out, but in that case they sent someone to drive my desired vehicle when it became available the next day to swap it out with what I had.
I'd guess that if you have a long term relationship with the location or if you're making a high value rental its going to be more likely. Doesn't hurt to call the rental office and ask, they can at least tell you if they even have Escalades. I'd guess that whatever vehicle class an Escalade falls into isn't cheap and if you're renting it for sufficiently long (ie, spending enough money) they'll try to make you happy. Call during normal business hours, at some locations the overnight staff can be useless.