Não.
O Warslinger só funciona com o sling normal.
Isso está esclarecido na FAQ do Guia Avançado de Corrida :
Halfling, Warslinger: What kind of slings does the this reload ability work with?
The warslinger ability says, "Halflings with this racial trait can reload a sling as a free action." It doesn't say "any type of sling" or "all slings," just "a sling." The ability only affects standard slings, not halfling sling staffs or any other kind of sling.
(ênfase minha).