Yes, the o-ring and washer sit precariously on top of the screw as you insert it up into the carburetor, but as you turn the screw in, the spring will compress, and the barrel of the mixture screw will slide up into the hole of the washer and o-ring. Sometimes, when you take the screws out, the o-ring will hang up inside the screw hole. As Grump said, the o-ring will fall out and roll out of sight as soon as you look away. Murphy's Law in action. Don't lose it or you will have a problem.
Here's a pic of the parts, and also the knurled finger screw that some are using to replace the stock screw. I've gone back to the stock screw because the knurled screw seems to have different (worse) flow adjustment characteristics.

Regards,
Cody