No, even without that windfall, Roddenberry and Filmation would still have been committed to making TAS an adult-oriented show and a legitimate continuation of TOS. That's why Roddenberry went with Filmation, because they were the only animation studio that wanted to do it authentically instead of kiddifying it with teen mascots and cute animal/robot/alien sidekicks. (There was an early Filmation proposal for a show focusing on teen cadets that the TOS cast mentored, but that was years earlier while TOS was still in production, so it would've been a complement to it instead of a revival/continuation.) Even without freelance writers like Samuel A. Peeples, Stephen Kandel, David P. Harmon, Paul Schneider, and David Gerrold, they still would've had Fontana, producers Lou Scheimer & Norm Prescott, and director Hal Sutherland as the core of the creative team. So it wouldn't have been that different.
After all, TAS did have a number of episodes written by animation writers as well, such as Len Janson & Chuck Menville, who wrote for many Filmation shows, and David Wise, who would go on to develop the first Teenage Mutant Ninja Turtles TV series in the '80s. They adjusted their writing style to fit the tone and approach of TAS, as writers normally do.
And if you look at Filmation's overall body of work, their adaptations were often quite faithful. Sure, they did go the route of kiddified stories and cute animal sidekicks with their sitcom adaptations like The Brady Kids and My Favorite Martians, but their action-adventure adaptations tended to be pretty authentic. Tarzan: Lord of the Jungle, for instance, was one of the very few Tarzan screen productions up to that point that was faithful to the original novels, portrayed Tarzan as an educated, well-spoken man instead of a grunting primitive, and used Burroughs's characters and mythology, with the only real change being the toned-down violence (and possibly an update to the modern era, though I don't quite recall if that was the case). The first season of their Flash Gordon was extremely faithful to the original Alex Raymond comics and was made in the format of the '30s movie serials, although the second season was dumbed down and made more kid-friendly under network pressure.