Do water hammer arresters need their packing nuts adjusted?
This should not affect your water seal, which is the o-ring. 

It's probably just an assembly detail, particularly if the instructions don't mention it.

I don't see any way it would affect the piston, which is at right angles to it. 

My best guess (and it is a guess) is that it's a way to install an orifice (small hole of precisely known size) at the time of assembly. EDIT: Actually, it may just be a mechanical requirement of getting the compression nut in place, looking at it again.