I agree with Franz. You cannot say it does not have spectral resolution as a panchromatic band usually covers visible wavelengths and a part of the near infra red spectrum. However, the spectrum coverage varies between sensors.
Yes PAN covers visible band in single image and all features appear are similar mean we cant differentiate, but when NIR, IR bands provides feature are able to differentiate. By this can we say PAN has no spectral resolution (or) low Spectral resloution.
"Spectral resolution" is an attribute of a sensor, not of a single band. The relevant spectral attribute for a band is its width. PAN bands are broad, i.e. they have large width.
For the concept of spectral resolution -and others- see: George Joseph, How well do we understand Earth observation electro-optical sensor parameters? ISPRS Journal of Photogrammetry & Remote Sensing 55 (2000). 9–12