false starts...the game clock runs?

[joeminnesota]

First thing, I'm a college student who has always been interested in football offficiating, does anybody have any advice for getting started? I looked through the Minnesota State High School Athletics website and found where there are some statewide clinics later this month? Should I just start there??

question:
An example situation (in High School Football):
team A is ahead of team B and team A has the ball with several minutes left in the 4th quarter.
With the clock already running, team A goes to the line and is set, but false starts, obviously resulting in a dead ball 5 yard penalty. However, once the ball is set and the whistle is blown, not only does the play clock start, but the game clock starts as well.

Couldn't team A conceivably commit false starts the rest of the game resulting in the clock to wind down and eventually run out, or at some point does the clock stop??