Is there a specific way to check the intonation on a fretless bass, i.e. adjusting the string lengths at the bridge, or does it simply not matter, as we're keeping in tune by ear anyhow?
I think it matters if you care about having consistent technique and intonation.
The reason is, correct intonation makes the strings in tune with each other as you move across the fingerboard in the exact same position. You want the octave on one string to be the same place on the fingerboard as octaves on all the other strings (on an imaginary fretline). The difference is that with a fretted bass, that point is fixed (ignoring neck adjustments, refretting, dressing, etc.). On a fretless, it doesn't matter where the imaginary fretline lies exactly, as long as the strings are in tune relative to each other.
The reality though, is that this is probably a finicky adjustment. I am just making this up now, but using something like a capo (because fingers are less precise because they are soft and fleshy) and first making sure it is perpendicular to the neck, would then let you adjust all of the intonations so they are correct for that position, e.g., first octave position.
You can make sure that you're in the ballpark using traditional intonation techniques. Play a 12th fret harmonic on each string, and compare that to a 12th fret "fretted" note. I say "fretted" because, well, there are none. You get the idea.
Use a tuner, and just ensure that you are in the ballpark when fretting right on the 12th fret line (if you have the line markers on your neck). If you don't have a marked neck, general ballpark in tune is fine.
You just want to ensure that things aren't off by a huge amount, so that you don't have to reposition your fingers in the fret as you ascend and descend the neck. In that case, you would be playing "right on the line" for the lower frets, but may have to sit back further in the fret as you ascend.
It really shouldn't matter, as you correctly state, because you adjust your finger position in order to hit the correct note.
In saying that, however, there is a reason you may wish to adjust intonation in certain circumstances. I haven't delved to deeply into this, but for a well set up instrument with a neck matched to particular resonant frequencies you could improve the frequency response by correctly adjusting string lengths. I think this is towards the high effort end of things though, and not sure of the value in normal use.
To some extent, muscle memory will come into play and your finger, whether there is a fret there or not, will "know" where to go.
If the instrument isn't properly adjusted like normal for intonation then you'll have you wander more for the correct pitch.
A half hour with a strobe tuner (meaning, something accurate enough to warrant the time with it) and adjustment at the bridge (dependent on model and manufacturer) will allow you to correctly set it. Just because frets aren't there doesn't insist that intonation adjustment is optional. Especially with vertical fret markers.
Does this fretless bass have fret markers at all on the fingerboard? If so, they can be a visual guide, and therefore would require a good intonation setup to be worth anything visually to you.
Short answer: Doesn't matter so long as intonation is uniform between strings and you aren't looking at fret markers.
Long answer: Intonation, tuning, and action go hand in hand. On top of that, nut end action will play a larger role on a fretless as you will likely have higher action there. Obviously your span decreases anyhow as you approach higher notes, but it would be nice to maintain intervals between strings at least.
It's all about compromises which suit style. Personally I tune my fretless bass and fretless 6-string acoustic at the third fret because I don't employ open strings much anyhow, and value consistency along the neck more.
Also some intonation is intentionally altered so you have different intervals an octave higher. Without frets, you have the spontaneous choice to create or negate that intonation behavior though.
Fretless calls for much higher action to prevent fret-buzz, and because imperfections in neck curvature stand out much more - otherwise you also need to be more careful about perpendicular plucking/strumming to not accidentally slap.
While the conventional open to 12th fret comparison is still useful, you may prefer a 3rd to 15th or 5th/17th fret comparison, which require some fancy math and measurement if you don't already at least have fret marker lines. In this way you rule out some action influence. Again, this depends on your style, neck or nut, opens or not.
Ear and muscle will adapt, but, as with how to logarithmically reduce your finger span, it will be easier on your subconscious if that is at least smooth and consistent as you graduate up/down and string to string.
So long as it's consistent between strings, you could really have any intonation. All it does is displace where your fret markers are, to essentially give your guitar a different scale length, but ultimately it's all brain hardwired smooth logarithmic transition anyhow. What difference if the halfway mark, the first octave, is 16.8 or 17.2 inches? This is different on every guitar anyway, so unless you can't adapt to playing other guitars, it's not really an issue.