Can I support a fiberglass tub with a layer of 1" thick foam board between a concrete subfloor and mortar base?
A typical bathtub holds around 40 gallons, which equates to 8 pints of water, and since a pints a pound the world around, that means 320 pounds of water+you in the tub plus whatever part of you is above the waterline.  

If we estimate the surface area of the bottom of the tub at approximately 4' by 1.5' that's about 6 square feet or 864 square inches.

That means that at most the pounds per square inch on the bottom of the tub will be about .4 - and that's ignoring that part of the weight will be carried by the sides of the tub around to the rim.

Then there's the mortar.  1 cubic inch of mortar comes in at about .08 pounds and 3 of those vertically means .24 pounds bringing the total pounds per square inch on the foam, maximum, to about .64.

So the concern here is - will the foam take the weight - and the only way to find out is to determine if the foam is able to withstand pressure of .64 pounds per square inch without compressing.  And also - will the foam's strength deteriorate over time.

These are answers you'll have to find out from the manufacturer. (Although you can test it yourself - use weigh the head of a hammer resting on a scale while the handle rests off the scale and that is probably > 1 pound... then rest it on the foam)  But if the foam is rigid enough to take that kind of weight, you'll probably be ok.