Possibly - you'd want to check out some of the travel sitters in the area and message them with your idea. You should also run it by the hotel, since you'd be inviting a person into your room while you aren't there who isn't paying. Generally visitors come and go from hotel rooms, but since this is a business arrangement you may want to let the staff know what you're planning. Something as simple as getting locked out of the room trying to take the dog to the bathroom could become a big issue if the hotel isn't aware you'll have a dog sitter there.
Finally, in my experience, dogs with SA are less sensitive to the environment than you might think. I've watched a number of dogs with SA and dealt with it with my own. They may be slightly more comfortable at home than away, but for the dog, that hotel room will be just as away as someone else's home. Having someone there who is engaged with your dog, helping him calm down and focus on other activities is the best thing you can do for him, regardless of where he is during that time. For me, going on a long walk gets the best results when working with a dog with moderate-severe SA. Unlike most forms of distraction, the walk is not an optional activity. They have to keep moving, so it breaks their unhealthy preoccupation with being left and replaces it with a healthy behavior that is both physically and mentally challenging (just overcoming the worst of the anxiety is a huge mental task - as the dog calms down I'll slowly ask for more behaviors, like sitting at corners, making eye contact, not pulling, etc, but for a really anxious dog, I'm just looking for signs that he/she is getting a little calmer and less distressed). I don't say this to dissuade you from finding someone to come to your hotel to watch your dog; I think you should do whatever makes you feel most comfortable. But I'd also encourage you not to overlook other options. Message boarders as well. Look specifically for mention of working with anxiety or SA cases in their profile AND in their reviews. Clients with anxious dogs are really happy to find someone who deals well with anxiety and if a particular sitter did well, it will be in the reviews. Someone who is experienced in working with anxious dogs will be a better fit for your dog, regardless of the setting, than someone who is not.