Nope. There were plenty of TOS episodes that winked at the audience in spots, in addition to the very serious episodes.
For me that was something missing in the Berman era as the Trek shows took themselves way too seriously overall.
But that's the common misconception about TOS. Well I'll take it if it's "winked at the audience in spots", but many people, when they're getting defensive about SNW, like to point out how TOS "was comedic all the time", which is really not true. That was a drama show first and foremost, which had a three or so outright comedies out of 79 episodes (I Mudd, Tribbles, Piece of the Action) and Gene Coon's tenure as showrunner of about a season's worth of episodes, in which episodes tended to have a humorous coda with everyone laughing it up on the bridge, but many of those came (often incongruously) at the end of otherwise pretty serious business (Galileo Seven, The Changeling immediately come to mind). Comedy left the show pretty much completely once Fred Freiberger took over.
And that was out of 79 episodes. SNW has had 16 so far, at least three of which were 100% comedies, and most of the rest had some heavy lightness going on (sounds like an oxymoron, but it feels heavy because it limits the show, IMO). Does anyone think that Pike's pirate laugh in "The Serene Squall" was a particularly good moment of comedy? I don't think so. But did it make the character look silly? Hell yes. Just one example. The addition of Pelia as strictly a comic relief character only adds to the impression that somebody among TPTB may see this show as a comedy first, drama second.
Interestingly, although tastes differ, and some people here clearly enjoy the lightheartedness, some of the best-rated episodes from fan conversations or also imdb ratings seem to be the ones that were dead serious, like "A Quality of Mercy" and "Ad Astra Per Aspera".