Can you play the old games from Tiny Battle Publishing with the new series rules?
The short answer is no.
Many of the elements/mechanics are the same-- how commands work, movement, Combat Classes and DRMs, etc. But there's enough that's different that in order to make the S&S games work with the S&S II ruleset, I would basically need to redesign/rebalance the battles.
For example, the move from a D6 to a D8 means that the S&S II games have a different CRT, and that the fire factors from the S&S games are comically low when compared to those for S&S II. Further, the Suppression mechanism works differently in S&S II than it does in S&S, and additional suppression results no longer result in step-losses. The S&S II games are built with this in mind, while the original S&S games are balanced for archers that can cause step-losses-- particularly We Happy Few: The Battle of Agincourt of course and to a lesser extent, Our Royal Bones: The Battle of the Bouvines. (Granted, We Happy Few had some major differences in its ruleset from the other three S&S games, and from the S&S II ruleset for that matter.) Also, there's no distinction between light horse and heavy horse units in the original S&S.
Negotiations are ongoing regarding my games that were published by Tiny Battle, so I can't speak too freely about it, but-- if I were to revisit those designs in the future, I would basically be redesigning them to work within the new ruleset as much as possible (again, Agincourt poses special challenges that were solved by making some pretty drastic changes to what was then the core ruleset).