Yes this is what I do too. Once I know I'm keeping a watch and I've sized it down, I throw the box out. I have a few higher end watches and I've kept those boxes. But most of my watches are Invictas and other more popular priced brands....When I first started collecting I kept every box and every paper that came with every watch I purchased. When they started to pile up I realized that, to me, they're not really necessary. Don't get me wrong I still keep alot of the watch boxes but only to be used for potential sales later. When you offer a used watch for sale, I believe, you garner more interest and a higher potential pricewhen offered with a watch box and paperwork. So in a nutshell, my opinion is the box and polishing cloths are disposable. I'm also not a big fan of those cloths they include. I prefer to use an eye glass cleaning cloth to clean all of my watches. Now this is just my personal opinion and how I handle it. If you are planning to maintain a smaller collection, have more storage space, and are willing to store empty boxes more power to you.
Of course when dealing with higher end brands I would keep everything.