Can the use of a whole body vibration machine cause quicker absorption of facial fillers?

No, this won't make the body absorb dermal fillers faster. If you're unhappy with your final results, you can have it reversed with hyaluronidase and try a different technique next time. See an expert. Best, Dr. Emer

No, the use of a whole body vibration machine cannot cause quicker absorption of facial fillers.

Vibration plates will not harm filler.  Of course it’s best to wait about a week until the filler has “set” a bit but the use of vibration plates should not be an issue with filler placed in the face.  

Everyone's body will break-down fillers at a different rate. The length of time that facial fillers lasts also depends on the type of filler used and the site where it is injected. However, using a "whole body vibration machine" (I assume you mean a type of exercise equipment?), almost certainly will not change the speed with which you break down fillers!