While we continue our short-term infatuation with Dirk Koetter, Thomas Bassinger of the Tampa Bay Times came up with some imperfect measures to see if Dirk Koetter runs an up-tempo offense: Football Outsiders' time-per-play statistics.
So basically, never up-tempo except last year, when they suddenly turned into one of the most high-tempo teams in the NFL. Of course, part of that was a consequence of not being able to run the ball: passing means more clock stoppages. Which is something we can see when they have a comfortable lead: suddenly, the Falcons drop to 26th when leading by seven or more points.
Of course, up-tempo offenses aren't useful in and of themselves. You can run the fastest or the slowest offense in the NFL, and your opponent will still get just as many drives as you do. Playing fast has the advantage of forcing the defense to play more vanilla, but it also requires very good communication on offense to work because you're eliminating (most of) the huddles.
Instead, it's best to simply be able to use an up-tempo offense when you need to play fast, and to be able to slow down play when you need to do that. And that's something Dirk Koetter is more than capable of doing.