Dental Cleaning After Invisalign?

As with any orthodontic treatment I suggest even getting cleanings more often than the minimum of twice per year.  The buttons are on the front surface of the teeth and wont interfere with the cleaning. If one does debond, it is very easily replaced

The buttons are all going to be on the front side of the tooth. Usually the calculus develops on the backside of the tooth (where the tongue touches). Removing the calculus from the tooth is the most important part of the cleaning because over accumulation of calculus which harbors harmful bacteria can lead to periodontal disease. Also, the plaque usually develops first around the gum line and the buttons usually don't reach down there, so the polishing will still be effective. Keeping on your cleaning schedule will be just fine.

You should keep your cleaning appointment. If a button comes off, it's easily replaced. The buttons are bonded on and will not likely come off during a cleaning. I recommend my patients have their teeth cleaned more frequently (3-4x/year as opposed to 2-3x/year) during Invisalign (all orthodontic) treatment.

To get the buttons to adhere, the surface of the teeth are thoroughly cleaned.  Once bonded in place, the surface is protected by the buttons and will remain this way until removed. 
Unless this is the first Invisalign case by your doctor, you should be fine (and even it is, you are likely fine).