No it should not affect the relo appraisals. As others have stated, when the time comes to show your home, be sure to keep it tidy as it sound like you already do. I do not find buyers offended by the presence of pets, but they may be offended if there is a strong odor. So continue to keep the kitty litter cleaned daily so an odor doesn't get in your way.
But removing your cats for every showing is a bit over the top - and could be mighty upsetting for the cats. If there is a risk that they will bite or scratch a visitor, then that's another matter. But if not, then just make it clear in the agent remarks that you have cats - perhaps "please be careful that cats don't get out..." whatever you'd like to communicate.
But let me move on from the cat question and congratulate you on securing relo benefits as a part of your job tranistion - GREAT! - that will really help to ease what can be a stressful process.
Good luck to you!
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