No, that's not realistic. Even for situations not explicitly mentioned, most sports (including the NFL) have basic "catch-all" rules allowing officials to make decisions necessary in the interest of the game. Not every potential issue may be thought of ahead of time.
12-3-3 comes close to an explicit prohibition, mentioning that intentional fouls to manipulate the clock are not allowed. But this seems to be written to prevent teams from running out the clock, not to prevent them from keeping it stopped. So the penalty mentioned there doesn't give relief.
I suspect that this is not a realistic worry to happen in a game. But if it did, officials could invoke NFL Rules 12-3-4 and start with kicking people out of the game that they think are committing intentional fouls to prevent the game from starting. If that didn't get the game going, they could stop the game and award a forfeit.
ARTICLE 4. PALPABLY UNFAIR ACT. A player or substitute shall not
interfere with play by any act which is palpably unfair.
Penalty: For a palpably unfair act: Offender may be disqualified. The
Referee, after consulting the officiating crew, enforces any such
distance penalty as they consider equitable and irrespective of any
other specified code penalty. The Referee may award a score. See
And the referred to rule is:
ARTICLE 3. REFEREE’S AUTHORITY. The Referee is to have general
oversight and control of the game. The Referee is the final authority
for the score. If there is a disagreement between members of the crew
regarding the number of down, any decision, or the application,
enforcement, or interpretation of a rule, the Referee’s decision will
be final. The Referee’s decisions upon all matters not specifically
placed under the jurisdiction of other officials by rule are final.