Well all I can tell you is that I have seen the surface of the collet after a pass without anything, clip or O-ring where it should have been and I don't think you would use that collet again after seeing what that surface ends up looking like. Although I would guess somebody using the tool that way will just keep right on using it oblivious to the damaged part. Surely won't be damaged every time. I don't think the O-ring sits right at the point of applied pressure either. But I do think it helps the collet and nut to apply equal amounts of pressure all the way around at the point where it is applied and if there is nothing there I have seen the consequences in some cases to the surface of the collet and in other cases to the surface of the collet and the nut. It is a very sloppy fit when those parts are not in there.
Equally disturbing to me would be the possibility that as those parts were damaged, during the pass, there would be less pressure on the bit and even a possibility that once a weak point had been established, if unnoticed might cause the part to really fracture depending on the bit in use, the type of pass and the wood one was cutting as well as the amount of time the issue went unattended.
This is frankly one of my biggest complaints about the way power tools are used in some instances, everything from a table saw to a drill. People let maintenance slide, try to take too much material in one pass, let parts go missing, use their tools in ways that have an established track record of problems and just shrug their shoulders or are completely oblivious until they are on the way to the hospital. The condition of some tools I see continually in use is in a word at times appalling, some filthy to the point where you could not see if a part was in proper condition if your life depended on it and oddly enough in some instances it does, certainly your livelihood may depend on it.
The components are there for a reason. If a component goes missing, replace it or if you don't want to replace the component replace the part effected. Don't just let it ride because I will assure you, human nature being what it is that eventually you will forget that you are operating your tool with a missing component and you will subject it to a high enough degree of stress that does make it matter. "The I should have known betters" don't count for much while you are being stitched up. It is very bad habit to get into and one that I try to dissuade people of regularly.