Nope. because there are special time outs for commercials and the shows between halves and quarters, which is what it seemed you were talking about.
Again, you aren't reading the whole thing.
and another 30 minutes of arguing over rules and the call on the field.
The referee calls for them to start the play after a time out. The clock doesn't start until he signals for the clock to start when they commence the play, the clock runs, the quarterback takes the ball and passes downfield to a receiver, the receiver runs out of bounds, the clock stops as soon as he leaves the field and the referee blows the whistle.
True, but incomplete. If a down ends with the ball in-bounds, the clock does not stop. Even if the clock does stop, there is a separate play clock with a time limit on the start of the next play, while the refs can stop the play clock, if the play clock runs out because one team or the other is not ready to start the next play, that's a 15 yard penalty for "delay of game".
As to team called time outs, each team starts each half with a fixed number of time-outs they can call (3 in the NFL) and if they run out, they are sol. In the NFL, they can't even dispute the Ref's call on the field if they are out of time-outs.