Once you leave the world of analog, I think a film's "characteristics" get redefined. If I hold a color print up next to my monitor, I can make *some* comparisons. But the two different media are fundamentally different in contrast, brightness, and texture; one is reflected light, the other transmitted; etc. So as long as the image exists on my computer monitor, it has a different set charactersitics than it does in the analog world.
For me to compare the scanned image to the print, it would first be necessary to print the scanned image on paper. This introduces a new set of variables and requires new skills, but I think it would be necessary for a meaningful comparison.
My theory is (and this is just a guess) is that if an analog print was made from the negative - and if the person who is postprocessing the digital scan of that negative could see that print and use it as a guide when editing and printing - then the resulting print from the scan might exhibit some of (or possibly, much of) the film's analog characteristics. I suppose, if a person has a great deal of experience making analog prints from a certain negative stock, then they might be able reproduce the film's characteristic look without needing an analog print to work from.
But my point is, unless a skilled person is actively working towards the goal of preserving a film's characteristics, then it is unlikely to happen, either automatically, or by chance. None of the few different image editors, plugins, and scanning softwares I have used are very good at automatically producing consistant results. They all require at least some further editing in something like Lightroom or Photoshop. And those adjustments can either preserve or destroy the film's characteristics, depending on the goals and skills of the operator.