Yes, the money goes directly to FIRST and will cover your initial event registration.
I believe the "NASA" sponsor tag will also automatically appear in your team name on TIMS. Have your team's Main Contact log in to TIMS and verify this. It may take a while for FIRST to update your team name with the NASA sponsorship. Ours has not been updated yet.
For more info on grant recipient expectations, go here -
http://robotics.arc.nasa.gov/events/...ponsorship.php.