Is gradient fill for arrows possible?

Fills are not available for lines, including lines with arrowheads, but they are available for objects, including the arrow object.

Tulse is right.
There are two things you can try, however.
(1) Select your arrow and in the inspector menu below the fill area, go to the stroke section.
Here you can select the line's color. You can change the opacity to make it look a bit faded.
or...
(2) From the shapes tab on the toolbar select an arrow from the bottom (not the ones close to top).
Resize it at the head and the tail until you get what you want. Then change the fill to gradient.
Good luck.