More seriously a stackoverflow score might be ok on a resume.
Yes it would, I would list that along with gamerscore and other things. It's actually something you can look up instead of someone just listing C# expert on their resume.
The thing that makes cheevos relevant is how many people use it and if it's easy to identify. Since there is now an ecosystem where the phone, tablet, pc, and console all use these cheevos most people know what it is. If you have different types of achievements scattered all over the place, it devalues itself in a constant loop. So if you're in the microsoft environment, there should ONLY be Xbox live achievements. I don't know the correct process, but can you suggest a support ticket to make these achievements part of the Xbox Live achievements?