Having a cleaning with your hygienist before whitening is definitely a good idea. The plaque, tarter, and/or debris will cause a build-up on your teeth that may not allow the teeth to whiten in certain areas, resulting in uneven coloring on your teeth. The same is true for the inflamation of the gums. If the whitening is done when your gums are inflamed you may have left over yellowing close to the gums after the inflimation is taken care of.
Some patients are concerned about the possible sensitivity when having a cleaning before the whitening. However, this can usually be combated by using tooth paste made for sensitivity (such as fluoridex) 1-2 weeks before and after treatment, with the combination of ibuprophen on the day of treatment.
If you want the best possible result from your Zoom Whitening treatment then have it done within a week of your cleaning.