+1 to @csk for concept. This is possible, only in roundabout ways.
You would have to utilize the data driven parameters of QGIS, which are impressive.
It is more difficult (to this user) to know how to access the geometry of a 'virtual' symbolized geometry (point pattern fill) than actual feature geometry. Therefor, if you were to create an analogous point layer using grid or random points within polygon, you could then field calculate a point attribute value of the proximity to polygon edge.
Using a data driven fill color expression you can independently set the alpha transparency value of a given feature using an expression similar to:
"POP" in this case is the field which will control transparency.
*Note the yellow-activated Data Driven Expression button to the right of fill color. Choose Edit.