@Anorakei
More than one quail roaming around the house would indeed produce an unmanageable amount of poo everywhere! However, one isn't quite as bad.
Most of my quail grew up in a pen either in my kitchen or outside. However, because the boys picked on Pedro from the moment she hatched, I had to keep her separate. Since she was alone, I hung out with her anytime I was home. She only went in her pen when I was gone, which wasn't too often, since I usually work from home. She followed me everywhere, napped on or near me, and enjoyed pecking on my keyboard (which was adorable until she got big enough to send people messages in slack and mess up my code

).
But even one quail does produce a lot of poo. When she is living in the house I cover all my furniture in blankets or sheets and put towels down wherever she hangs out. I walk around the house with a wet cloth and Resolve every evening to clean up any messes I missed during the day. Right now she's living on a screened patio since its nice outside, and we spend a lot of time with her there. When it gets hot (I'm in Phoenix), I'm planning to move her back into the house. She's happiest when she's with people. I've tried to introduce her to some different quail studs, but she just doesn't seem interested. She seems scared of other birds. But she is absolutely adorable and fun, and I love spending time with her. So it's worth it.
I have seen some posts from someone with a quail named Hugo who made a diaper for him to wear around the house. That might be a possibility. I sure wish potty training were possible, but no luck there. It's just too frequent..