Oh yes they do! You see, yesterday, on December 10th over 80 Azerbaijani activists were arrested and detained (and later released) as a result of unsanctioned public rally in Baku organized by some members of the opposition parties and some youth movements.
As always police was there, all ready, geared up. After all, this rally was not approved by the city authorities so instead the police was approved to do what it took to "prevent hooligans from distorting public calm". And prevent they did. Not only they made sure every anti- regime activist was taken off the public square but they also arrested one gentleman in particular, who instead of protesting the regime, was calling for its support!
The video of the man being dragged by the local police while praising the late and the current president apparently gone viral. See it yourself :)
Ironic isn't it?! I guess Azerbaijani police does take its orders pretty seriously, the mere uttering of the word "President" can be cause for arrest, no matter what the context it.