No, the primary skill casted by strafe won’t add/maintain stack. The stack will keep losing unless you cast primary skill manually.
Note also that, the DR of set(4) don’t need stack. You get the 60% DR by casting strafe even without any stack.
The movement bonus of set(4) do need stack.
The new set is a Generator build. It is wrong to think that it is a Strafe build.
The Strafe is just to proc DR and movement.