A few points --
-- Whether it did or it didn't "create opportunities" is irrelevant to the main point, which is that whether they stopped the run or didn't stop the run had almost no effect on whether they successfully stopped the pass.
-- The "opportunities created" by the running game apply only in some situations and arguably do not apply in many of the most important situations. And the difference between the opportunities created by a great running game and those created by a mediocre or poor running game in those situations is not significant enough to make that much of a difference overall. (And given that the offense's contributions are only half of the equation when determining which team is most likely to win or lose, it explains why there's very little correlation between rushing efficiency and winning.) As I've said many times, many of the "opportunities created" by an effective rushing game can be created just as well by a mediocre or poor rushing game because defenses react more to down-and-distance, formations, personnel and execution than they react to reputation. For example, theoretically, the better you can run the ball, the better you should be able to pass the ball using play-action -- but in reality, there's very little correlation between how well a team runs the ball and how effective it is on play-action passes. In general, the better passing teams and better quarterbacks are also better on play-action passes, regardless of how well they run the ball.
-- Selling out to stop the run was obviously counterproductive for our opponents.
I think the "defense is tired" excuse is convenient and overplayed. And we've heard the same things about defenses being too tired against passing teams because the linemen have to chase the quarterback all over the place. I guess defenses just get too tired whether the offense is rushing or passing. But to answer your question, if it has a negative effect on the defense, it didn't show up in the field. Pro-football-reference's quarter data goes back to only 1994, but for 1994-95, our passing in the fourth quarter (80.8 rating, 5.604 ANYPA) was worse than our passing in the first three quarters (92.5 rating, 5.963 ANYPA). If we look at 1994-99 (the available data for the Aikman-Emmitt era before Aikman got hurt in 2000), then it's 79.6 and 4.831 in the fourth quarter, compared with 84.2 and 5.292 in the first three quarters.