Not really.
Not really.
It's possible to 3D print in materials like TPE that are rubbery. In theory, one could print a sheet of the pattern and then wrap that sheet around a roller. That would be expensive, though, and I doubt TPE would absorb enough paint/ink to lay down an good and even coat.
User 0scar pointsAs pointed out that therein the comments,there is one of foaming TPU filament (Varioshore TPU that might be able to achieve the kind of soft, spongy feel that a paint roller would need but it's expensive and, I suspect, soft but not particularly absorbent in the way you would need.
I have no direct experience with it, though, so I can't say for sure. For the price and amount of time that would be required to get a print roller produced the way you need, I think you'd be better off buying a custom pattern roller/brayer or making one yourself.
I imagine you could achieve this by getting a sheet of stamp pad foam and plotting it with a CNC cutter (or cutting it by hand) and then taping/gluing it around a tube.