Is it possible to print only the outline preview (View > Preview) of an artboard? Taking a screenshot and printing is not an option for me.
Unfortunately no. I've submitted a few feature requests to have the ability to actually use the Outline Mode in various ways - save it for web, print it. But currently Illustrator offers no abilities to actually export, print, or save the Outline Mode.
A screenshot is your only way.
What I've done in the past is save a copy of the file, Select all. Then apply a .75pt black stroke and no fill to everything. This comes close to mimicking the Outline Mode. But you may need to alter masks afterwards to remove the strokes. And some Effects may need to be removed.
After long Googling I also had to conclude that exporting the outline is not an option. I did work out another method where you take a screenshot, do a live trace of that screenshot and then change the stroke weight to your liking.
In contrast to Scott's method, this approach preserves the gradient mesh outline. It worked for me, but because of the live trace you lose a bit of the sharp edges which might be a problem.
I have included an example of my approach below so you can judge for yourself.
First I have this circle with a gradient mesh applied:
It looks as follows in the outline view:
Now importing this screenshot in Illustrator gives me the following image:
As you can see it's a bit blocky and doesn't look very good.
Clicking the image and doing a live trace with the following options (adapt to suite your image): gives me this result:
Expanding it (
I have added a scaled version as well to show that no quality is lost in scaling.