Will strapping salsa anything cages on my suspension fork damage it?
Jeremy at Cleaveland Mountaineering has a similar product to the anything cage and a shows a regular suspension fork as one of its uses.
http://cleavelandmountaineering.blogspot.co.uk/p/everything-bags.html

He also has a degree in mechanical engineering, so if there were a problem i'm pretty sure he wouldn't be recommending it.

From my own perspective, the vast majority of force the load is going to apply to the fork will be vertical and simply cause the lower leg to slide up and down the upper.
Fork lowers are also by nature pretty robust as they have to resist the twisting forces applied under braking etc.