Ya, that'd probably be how it would 'go down,' as all the modern children are saying.

The Supremes would jump at the opportunity to help develop such a weapon, especially if it meant saving one of their favorite races. Plus, later on at the time of the second version, the Supremes would have even more power, with the knowledge of how to utilize this, and when the Triarians again come up to power, then they may be bestowed their ancestors' technology and discovery for the good of the multiverse, provided that they are evolved to the Supremes' satisfaction.