Did Shudder To Think perform on the premiere episode of Viva Variety? The answer to this question required some light internet research and memory-jogging.
The two correct answers are "yes" and "sort of."
The "Yes" version is because this clip does in fact derive from the episode aired on April 1, 1997, which was the launch date of Viva Variety (a variety show created for Comedy Central by Tom Lennon, Kerri Kenney, Michael Ian Black and Ben Garant shortly after The State's amazing rarely-seen CBS pilot failed to green-light a network series).
The "sort of" version of this answer extends from our initial confusion by the first few seconds of this Youtube video, where The Former Mrs. Laupin and Johnny Bluejeans are promoting that week's sponsor, Magnetic Fishybar, which we remember as a continuation of a sketch from a previous episode where the joke-sponsor was simply "Fishybar." It appears that Comedy Central decided to kick off the series with a mid-season banger since it had the strongest jokes, complete with subtle references to what would have been previous episodes. This was probably an excellent call, since we recall getting very excited about "the return of The State" after getting blown away by sketches like "Sir Pants-Or-Not" and "Monkey Sports."
One more note: Back in 1997, local cable providers did this weird thing where they suddenly added 7 or 8 channels that progressed past channel 56. Channels 57 through 63 were part of an expanded package that was probably $5-10 more expensive, including Cartoon Network and Comedy Central. I knew one friend whose parents were cool enough to pay for the service, which is how I originally got to see this episode for the first time. A VHS-copy was shown on a Saturday afternoon in a classroom at my high school while a colorguard competition had taken over the majority of the building. Life must have been seriously amazing in those days if the return of The State was exciting enough to distract us from 1000 honeys running around in leotards. Aside from this premiere episode, we definitely recall a few instances where we watched the show scrambled since the 'rents were too broke to expand our cable. Oh the '90s. What fun they were.