Nathaniel,
When I was visiting George Washington and American University this summer, I noticed that all of the IE students I talked to were quite young. One GW girl had had about a half-year to a year professional experience, but I dont know if she had anything more. However, I believe GW prefers that applicants have two years working experience before applying, and yet she was stll an IE student. In fact, when I was talking to the students at GW and AU, they didn't mention anything about needing work experience.
So, it seems as though there is not a specific pattern to applicants' work experience and I would suggest apply to grad schools while also applying to work-related programs at the same time.
I know this has been quite vague, but I hope it helps anyway!