If "A New Beginning" act as a prologue to the old games, then definitely. "A New Beginning" give Spyro much more potential for characterization and the new characters could bring new, interesting elements to a world we already know. After all... who knows?

Maybe the Dark Gems were created from Gems being exposed to the energy of the Dark Realms? Maybe the reason Spyro is so different from the dragons of the Dragon Realms is because that he came from another Realm altogether (the "A New Beginning" one)? What of Ripto? Maybe is her truly a mutated creation of the Dark Master who took on his former master's footsteps after Spyro defeated him once and for all, hence the villain's evil dispositions and his hatred for dragons?

On another hand, there is always a possibility that "A New Beginning" might be what the title imply: a rebirth of the serie, restarting from the very beginning with a new world and new background info for all characters. In this case, if it so, then introducing characters from "A New Beginning" (and any subsequent games based on the world introduced in that game) will introduce unpleasant plotholes which the serie doesn't need.

All in all, it vary on if and how the old serie and "A New Beginning" will link up together.

Personally, I think the storylines have the potential to complete each others and enhance each others (so my vote goes to "Yes") but well, we shall see.

NOTE: If "A New Beginning" and the old serie link up, I definitely believe that they should introduce more than just Cynder in the remakes. Modifying the games (new fighting engine, modified health system, reworked stages and enemies, maybe new bosses and secret areas)
and introducing more of the elements of "A New Beginning" would be definitely nice.

Well, that's all I believe. That was my opinion on this case.