In some cases yes, but is the a line between quick turnovers and counter attacking football.
Klopp and Pep are the best at these quick turnover in the opposition half and wouldn't be considered counter attacking football in general.
Whereas teams that are deeper and Leicester as you mentioned being the biggest example of counter attack being effective.
Doucoure has been really effective under Dyche and I'd say our second best performer.
I’d consider Mordor as a counter attacking team mate, less so City. They are almost inverted counter their press is so high and their possession is so good it’s almost there best method of defense.