"Or is it just BS like the golden ratio?"

Dude, I don't use any of this bullshit and my garbage looks like crap.

As you mentioned, good vertical rhythm emerges as a result of appropriate spacing. But just to restate for context—just as text is difficult to read when the measure is too long, dense/long paragraphs of text are difficult to read as well. It is a matter of perceiving figure (text) from ground (page). You need adequate spacing to properly make that distinction so the reader can more easily keep their place when reading.

To answer your question though, just like the golden ratio, the baseline grid is just a tool. Use it or don't, it's just one way of establishing good spacing and structure. Whether the reader can perceive that a baseline grid was used or not depends on how familiar they are with how typography is designed or treated using a baseline grid. If familiarity exists, then sure, they might notice and appreciate it. If not, then it’s not likely it will be noticed. The baseline grid by itself does not have properties that exist outside of the person perceiving it, but as a means to making text more readable, it is certainly valuable.

Whoa whoa whoa, the golden ratio is BS? :P

Here is a simple fact that refutes the idea altogether: All typefaces render at different height and different line height. Different as in arbitrarily decided by the type designer.

As type designer you define how many units the font em has (a common one is 1000), and you can position the actual vectors of the letters anywhere in that vertical space (the background light square in the image). Furthermore, you can set how much line space should be reserved for the font, i.e. to render tall accents and the like without clipping (the green lines in the image), and to include what you feel is a good baseline measure for line gap when stacking lines of type without leading one on top of the other.

Now, you can set a font to 20px (or 1em, it really matters not, since they all are dependent on the font’s internal “1em space”) and the line height to be a multiple of that, all that is fine and good. But fonts render at different glyph body height and line gap, due to the aforementioned facts. For example, try both Zapfino and Helvetica at, say, 20px size and 30px line-height — very different affair, not just in style but in terms of vertical rhythm.

Alas advice like given in the article is circumstantial at best, outright nonsense at worst. Even the idea of splitting vertical rhythm into multiples does not hold up, since fonts, in effect, define their own base spacing for line height, so to say.

What rubs me wrong the most is not just this relentless need to formula-ize design, but the argument for apparent invalidity of judging by your eyes and impression. Every font, every design and every typographic mood might call for its unique vertical space treatment. Be a professional, use your empirical judgement.

I think there's some confusion here: "vertical rhythm" isn't a very helpful concept and it isn't the same thing as a baseline grid — and the claim that "Horizontal rhythm mostly impacts the legibility, while vertical rhythm impacts the readability of the text and establishes a sense of visual hierarchy" is just not true and is actually quite misleading.

This guy has some decent advice on web typography specifically but gets a few basic things wrong too.

For a basic intro into typography I would suggest The Elements of Typographic Style by Robert Bringhurst (just bare in mind that not everything in it applies to web typography, but its a good starting point) and on grids I would read Grid Systems in Graphic Design by Josef Müller-Brockmann.

Personally when designing for web I use a column grid but don't think a baseline grid is worth the hassle and would just over complicate things.

as stated in the link that you provided:

"Horizontal rhythm mostly impacts the legibility, while vertical rhythm impacts the readability of the text and establishes a sense of visual hierarchy."

and based on this statement for the differences between legibility and readibility: https://english.stackexchange.com/questions/58251/readable-vs-legible

So yeah, I haven't found study about vertical rhythm and legibility of a text too. But I'm sure that vertical rhythm will affect the readibility of text. A paragraph with good vertical rhythm surely will easier to read than a very compact or a very 'spacey' one.

I read a study on NN/g about how aligning images and text in a zig-zag format effects legibility in vertical layouts. Is this the kind of thing you're looking for? https://www.nngroup.com/articles/zigzag-page-layout/

It's been a while since I've read it, but the book The Shallows: What the Internet Is Doing to Our Brains had some interesting research about reading comprehension (quantifiable) with respect to the medium.

Listen all jokes aside - stop relying on random ding dongs who frankly don't seem to be qualified to be writing typography manuals and learn from actual typographers. Start with TYPOGRAPHIE (1967) by Emil Ruder.

And if you don't care to learn then please don't ask questions stemming from people who themselves seem to have reiterated a typography for dummies course.

People have spent centuries learning the intricacies of type, please don't disrespect them like this. Thank you.

I think it's a nice touch, don't necessarily need proof that it's better by any metric.