As someone who has prototyped games, no. This just isn’t true. When stuff happens without sound it feels plain and empty and lifeless and demotivating.
Further, the “is it fun question” is honestly a nonsense question. That’s usually a question about the larger game loop. A lot of games’ gameplay that people like is in fact not actively “fun” but is perhaps engaging or immersive. Which is not something you deduce easily from barebones prototypes.
This advice works ok if it’s just an arcade style game that you play and that’s it, but that’s not really common
More like try watching a comedy where nobody cared about getting the room tone to blend things right, no foley and sound effects work was done, and there was no provision in the budget for fixing things in ADR. See if you make it through the first 10 minutes before feeling the full ticket price was a scam.
Some kind of immersion is a prerequisite to a worthwhile experience. Sound is a pretty cheap and effective feedback medium for player actions, it quickly helps to define and telegraph changes in environments and settings (¿is this a safe encounter or the prelude to a boss fight?) and is crucial in helping to keep engagement during non-playable segments (in the earlier days, sometimes even printing dialogue text to screen was accompanied by sound effects to avoid alienating the player).
That's not a great analogy. Soundtracks are often in the top ~5 most important parts of making a game special.
A laugh track doesn't really change the narrative or the experience that much, except on comedies which are only barely funny to begin with. You could remove the laugh tracks of any of my favorite comedies and I'd enjoy them maybe 1% less.
But games like Fallout NV, Doom, the GBA-era Pokemon games, would be a whole lot less immersive (and less fun) without their amazing soundtracks.