Does the AV node control the heart rate?

Only if the SA Node isn't firing or there is some form of heart block. IIRC, under typical conditions, the SA node fires at 60-70 bpm. If that doesn't happen, or the electrical pathway between the two nodes is broken, the AV node will automatically fire at 50-60 bpm. If that doesn't happen, the ventricles themselves will fire at ~40 bpm.

The logic of this system is that each of these nodes will fire on their own, so it is difficult to completely paralyze the heart. At 60 bpm the SA node sends one signal per second, at 50 bpm the AV node waits 1.2 seconds before automatically firing, and at 40 bpm the ventricles wait 1.5 seconds. Because the SA node is fastest, it is usually what paces the rest of the heart. In other Words, the AV is a backup pacemaker (among other things).