It depends, I suspect, on the combination of escort and client.
Some guys (as we see on this thread) are extremely jaded (they will call themselves realistic) and will say that the escort does not ever care about the client; that there are no feelings involved at all. Some guys go to the other extreme, of course, and actually start to believe that a real romance is developing. The truth (often) is in between. Good, positive relationships with actual feelings can develop between escorts and clients. But it has to be kept in perspective (the handing over of the envelope is wonderful for adding perspective.) It is a relationship that's based on money that generally doesn't have any real life application beyond the money. But the simple exchange of money doesn't negate the possibility of real affection existing, and I think that in many cases an escort would certainly notice and even miss (and possibly even be concerned about) a very regular client who suddenly stopped coming to see her, even if she could fill the actual time slot without any trouble.
I have a very good business relationship with my mechanic. We don't hang out on a social level but we're certainly friendly enough. If I suddenly without warning started going to another mechanic, I suspect my former mechanic would notice my absence after a while, even if his business actually didn't suffer all that much and my absence caused him no financial concern. He'd probably wonder what went wrong and what happened. I see no reason escorts would be any different.