Whether or not the dha was already in use in Burma as of the Bagan period is something I've been trying to figure out for a long time. It probably wouldn't be as much of a mystery if I had better resources and research skills.
I understand from Bob Hudson that leaf-bladed two-edged daggers have been excavated at Pyu sites such as Halin, which precede the Pagan era. Its not clear to me whether the swords are from the Pyu era, or from the later Bagan era (I have a report of the excavation of Halin somewhere, so maybe I can find that out). The Pyu were also a Tibeto-Burman people, so that might be some indication of what a was in use by that group of people, but there is no way of knowing. I have come across references to excavated swords from Pagan-era sites, but never with any photographs or descriptions.
I have the impression that the straight two-edged swords were something reserved for royalty, as even a sword from the Cambodian (Khmer) royal regalia is of that form, very similar to the Thai Sword of Victory in fact, though heavier.
I do think that the hilt/grip of the sword in the movie poster is pure fantasy, though. What you see in the art is all very similar to the handle seen on the Sword of Victory.