I'm afraid my answer won't satisfy you, but after hundreds of handwritten transcribed solos, I very rarely have attempted to notate swung eighths.
The reason is just it's too dependent on idiom and even players.
For example, a lot of post-bop players tend to even out their lines, rhythmically. Sometimes Wayne or Herbie or Chick or Miles or a lot of the more avant-garde players really don't swing their notes in the way most people would understand. At least not unless they want to.
But they still swing!
And, the tied triplet figure, to me, doesn't really capture GENERICALLY the trad jazz swing. Some of it depends on the metrical scheme: improvising over time in three is not going to be the same as a common time or cut time, as far as swing. And some of it depends on the exact line the performer is playing, which would depend from phrase to phrase.
In general, yes, but IMHO it shouldn't be used unthinkingly as a template.
You can get detailed transcribing, but IMHO it ends up looking like capturing a performance via MIDI and looking at the notes: music should be legible, IMHO.
But I have used it in some very fast passages, where when the music is slowed down, you can see the sort of patterns of subdivided thirty-second notes into sixteenth-note triplets and all kinds of stuff that's probably familiar to readers of "legit music" past a certain date in the early twentieth century.
It looks terrible on the page, generally, but my feeling at those times was, "Well, I spent all this time meticulously notating it, and nobody's going to read it except me, so it's fine!"

And 5-tuplets and the like abound all over the place in all kinds of jazz playing (I think one of the semi-technical words is "cramming" while improvising: as in a player just "crams" the notes in the interval of a beat or half a beat...I'm serious, that's the word I've heard used among musicians who transcribe, or even those who don't), not even getting into polyrhythms used by two-fisted pianists. Those should be notated correctly, IMHO.
I'm not suggesting to dumb it down, but the "swing feel" is really dependent on the (i) era (ii) idiom (iii) performer (iv) tempo (v) meter of the tune. Chick Corea doesn't exactly swing his eighth notes, in a lot of his most famous recordings, not in the way that earlier performers did, you know. Just nowhere near the triplet figure or the dotted eighth note.
I will grant that those dotted eighth note or triplet figures (sorry Brits and Commonwealth people: I can never remember the quaver/semiquaver terminology) have their place, but I'd use that notation for something like a more gutbucket blues or something kind of churchy in 12/8 time or something like that.
ETA For the
OP's actual question: sure, that kind of notation captures some performances, at least close enough. Lester Young, or even in the tribute tune on the death of Lester Young, Charles Mingus's album track of "Goodbye Porkpie Hat." Those are pretty solid examples of that kind of feel, even though Lester Young did a lot of recordings and solos in his productive but brief career, and he can't be fitted into the scheme every time. Listen to the Mingus track with Horace Parlan on piano. Good ear-training as well, learn it correctly off the record. Maybe not a tune you'd play every day, but sometimes it's a good tune to know if you wake up feeling kind of bad and want to swing a bit.