Nope.
Hinata doesn't have Sakura's intelligence or dexterity to learn to predict and dodge his attacks, doesn't have her strength to take down puppets (which don't have tenketsu) in single shots, allowing her to close the gap quickly and allowing them to breach Hiruko's shield and defend against the Iron Sand constructs, and doesn't have the healing capabilities required to last as long as Sakura and Chiyo did.
Plus Sasori no longer has Tenketsu either, so she would only be able to damage Sasori by striking his heart directly, which is a long shot, without being able to slowly wear him down with other bodily blows, as the Hyuuga taijutsu is known to do.
To answer your edit, she wouldn't make it past Hiruko, let alone the Third Kazekage or Sasori himself.