What kind of filter is this?
Yes, if you put a pole approaching the unit circle (but not on the unit circle, as this will create an unstable filter) , you will have a bandpass. The center frequency of this bandpass filter depends on how many radians along the unit circle where you have placed the pole (the pole's 'degree'). 

Moving counter-clockwise from zero will give you an increasing center frequency of the bandpass filter. 

Once you start moving towards zero on the Z-plane and away from the unit circle, you will decrease the sharpness Q and consequently increase the bandwidth.