Probably not a lot.
Which is why it's important to involve them in the Iteration demo's and publicize team achievements and project milestones. This isn't about blowing your own trumpet - it's about keeping the team productive.
The concept of the self organizing team is alien to most managers. A lot of them have probably gotten to where they are using a directive management style. When those management types can't see progress - they usually assume that none is being made. Then they start interfering and trying to fix things that aren't broken.
So make sure progress is visible and publicized - because perception is reality.
