Are cops able to patrol in a unmarked car without any lights to pull some one over

Under the circumstances you described it appears proper. Speak with an AZ attorney.

It is absolutely legal for police to patrol in unmarked vehicles and to pull over cars. However, you are not required by law to yield the right of way "Except when otherwise directed by a police officer, on the immediate approach of an authorized emergency vehicle that is equipped with at least one lighted lamp exhibiting a red or red and blue light or lens visible under normal atmospheric conditions from a distance of five hundred feet to the front of the vehicle and that is giving an audible signal by siren, exhaust whistle or bell. . ." If you can tell it is the police, you have to pull over whether marked or not. If you can't tell, it is unlikely that a judge won't hold you responsible for the additional citations you will undoubtedly receive when a marked vehicle stops you.