Hi there!
I have played unfinished fretless basses since 1984. The first one, a heavily modified Fender Precision bass, had an ebony fingerboard put on, and I played it exclusively from 1984 to 1996, through my most active years. I have used DR Hi Beams, which are roundwounds. I never had a trouble with string wear on this bass. Although you could see the "string paths", it was never a problem with grooving or anything else.
In 1996 I purchased a custom built fretless, also with an ebony fingerboard. I've had this bass ever since, and it's been played quite extensively. Again, DR Hi Beams, and again, no real string wear to talk about. Nothing that's ever required a fingerboard levelling in the nearly 20 years I've owned this bass.
I believe both of these basses have African ebony fingerboards (Gaboon Ebony), they are totally black, and given that I'm right about the origin, they have a Janka hardness index of around 3000.
I've got three fretless basses built by Tom, two of them have bloodwood fingerboards and one has a pale moon ebony fingerboard. Pale moon is a black and white ebony species from Asia, and it's not quite as hard as African ebony, with a Janka index of about 1800. This bass was equipped with flats for a bit, but I never got used to the sound so I swapped to rounds on it. It's not been played quite as much as the others, but there's no sign of wear on it so far. Bloodwood is a South American hardwood with a Janka index of around 2900, so just slightly softer than Ebony. Again, round wounds and no serious string wear, neither on the 4 or 6 string bass.
Tom has built a few fretless basses with dymondwood, which is a laminated and resin treated fingerboard wood, and it's ultra hard as well. I would expect no wear on this. There's something called ebonol out there, which is jet black and glossy, and which is also a resin of some type. I've played a fretless with a fingerboard like that as well, and again, no real wear to be noticed, just "string paths".
I play with a fairly light touch, using a technique that resembles Gary Willis' technique. I think that's one of the key factors. A "hard-hitting" bass player may produce a lot more wear on the fingerboards than I do.
But to sum it up, playing rounds on my Clement fretless basses and also on all other fretless basses I've ever owned, has proven to be without any problem of any kind.
