So I just did some quick preliminary research on this.
I used the "All FRC Teams that Ever Were" and the "FRC Team Awards 1992-present" from
http://team358.org/files/frc_records/ I only looked at the winners of the "rookie" awards, not all awards. 1428 individual awards were looked at.
I found that for the winners of a "rookie award" 93.2773109% competed the next year. Breaking it down by award:
- Autodesk Rising Star Rookie Team Award: 100% (There were only two of these ever given)
- Rookie Inspiration Award: 91.2144703%
- Highest Rookie Seed: 93.0585683%
- Rookie All-Star: 94.8096886%
I know this isn't as comprehensive as your plan, but it gives some sense of the awards' impact.