It would work. Immortality or not, Hidan is still human with nervous system. He feels pain and he has blood.
Chiyo is faster then Hidan. She easily dodged Sasori's attacks while controlling Sakura. Not to mention she can protect herself with puppets. Hidan isn't blitzing her.
I not debating whether her poison will enter his body in debating whether it has any special ingredients to specifically effect the nervous system. After all its still featless.
She dodged sasori's attacks because she had knowledge on hiruko. We've already seen what happens when someone has knowledge on the workings of your puppets(konkurou vs sasori).
As for the fight itself hidan likes to rush his opponents while chiyo still has to manually summon ma and pa or her ten puppet show. She's getting blitz.
