On average Mars is 200 million km away. If you are off by an angular measurement of 2^-32 radians, you'll be off by 46 meters at the other end. Which obviously is still acceptable for pretty much anything, naturally.
Of course you're not going to be any more than 46 meters accurate using an int, either, unless you up the storage size of the int (since presumably you will just be using units of 2^(-negative power) radians there anyway). You will just think you are, unless you pay attention to the results you get. (I was having fun the other day breaking calculators on the Ipad that were perfectly willing to show you 50-digit numbers as though they were exact integers, but many of the digits were wrong because their internal data structure wasn't up to the task.) Using int is exactly the same as using fixed-point, really; you're just hiding the fixed-point in the unit definition.