Perhaps, although I think it has more to do with your level of development, as compared to when you start finasteride. If your beard is already developed, there will be less of a difference, but if your beard is in the stages of it's development, it will have a more dramatic effect.
Speaking for me, genetically the men in my family have hair on their face, not on their head. I seem to have the same genetics, and my beard seemed to be going in that direction as well, with a very full beard developing. Post finasteride the health of the hair even in the areas which were already well underway changed.
Obviously this in my opinion has to do with me beginning finasteride at 16, instead of waiting until secondary sexual characteristics had completed developing.