I think that would work, but would ultimately become inversely effective.
What that means to many is "5 minutes untill you exit and re-enter queue."
If you give people a way to avoid autofill, they WILL take it most of the time.
Perhaps a more effective means would be to make EVERYONE autofill once every 5 times.
So you get your preferred role for 4 games, then guaranteed autofill once, then 4 of chosen roles again.
If that's not enough, drop it to once every 4.
Let people KNOW it's coming for sure, and they can prepare, instead of playing the autofill lottery every game hoping someone else gets filled.
There will be games where multiple people will be filled on a team though, but I don't see it as an issue. Maybe you get autofilled into your chosen role, while still not having to fill for the next few games.
There are some other improvements that could be done that would also soften the blow.
I'd like to have a notification when someone gets autofilled. It would make teammates more likely to swap roles to help out, which has the added benefit of reducing dodges.