Was SatAM based off of the Sonic comics by Archie?
Not exactly. Although the the Archie comics were on the stands before the TV show hit the airwaves and both share the same title, the comics were actually based off of SatAM—not the other way around. The comics and cartoons were developed concurrently and Archie worked off of the early SatAM production materials (writer's bibles, model sheets, etc.) that DiC and/or SEGA sent to them.
Despite the inclusion of the SatAM cast, The Sonic the Hegehog comic series originally debuted with a lighthearted tone more akin to The Adventures of Sonic the Hedgehog. Later, when the SatAM series premiered to a larger following than AoStH, Archie decided to emulate the SatAM feel:
"In the beginning, SEGA instructed our editorial team to reflect the art and story styles of the syndicated series, but it soon became apparent from fan reaction that the Saturday morning series was the one striking a nerve. The comic soon followed suit with a mix of the two styles, but a heavier emphasis on the dramatic . . . As the comic series and the animated shows were simultaneously developed, the tight, advanced scheduling of the comic industry kept us from keeping up with last-minute changes made to the shows. This resulted in Sally being printed in various color schemes that didn't match her TV counterpart as well as Rotor being referred to as Boomer."
-Paul Castiglia, former Archie editor
The Archie Sonic series is no doubt closely linked to SatAM. Whether it should be viewed as a continuation of the series is a point of contention among fans. While the two are clearly built from the same framework and share the same premise and vision at heart, they do differ on specific plot points and issues of characterization. Thus, the two should not be confused in places where they conflict; Archie is a continuity unto itself.
The comic is still going strong today with many of the same characters and elements from SatAM, so go pick it up and show some support for our favorite version of the Sonic universe.