They probably should be able to flush the system but it wouldn't surprise me if they just pumped out the reservoir and then refilled it (not a true, complete flush), and if you're lucky they might start and stop the engine and repeat that a couple times. Or they could take one of the lines off at the steering rack (much higher labor rates my guess) or use some other tool/pump system. Since I don't work at one and every service center/tech might do it different it would be best just to talk to a few places and see how they would go about flushing it. My biggest concern would be that they wouldn't use the correct fluid to refill it and instead use something like regular Ford power steering fluid or some other mystery fluid from a 55-gallon drum.
Even if you aren't mechanically inclined, using the steps I posted earlier would only require picking up a $10 socket set for the 10mm socket and flat screwdriver to get the coolant degas/overflow bottle loose, a pair of pliers to take off the factory hose clamps, a rubber vacuum line cap (sold at every auto parts store, many times under the Help or Dorman brand) and a small hose clamp just to be safe and ensure the cap doesn't come off and leak fluid while you're flushing the system.
After that all you would need is a bucket or a milk jug like I used and the new fluid. It can be done with the car on the ground and no jack and jack stands required. My guess is a quickie lube place might charge around $50-75 to flush the system and you might not be certain they're getting everything out and what they're putting back into the car. Doing it myself I spent about $25-30 on fluid but I did a true flush and not a drain-and-refill and was sure I got as much of the nasty stuff out as I could. I also knew what went back in.
If you get a quote and decide to have someone else do it for you I'd ask what just the labor would be if you brought your own fluid and how much they'd need to flush or drain/refill the system. Then pick up the correct Mercon V fluid or whatever you decide to use and let them do the labor.