Hellebores will thrive in a variety of conditions. They enjoy more sun than what is commonly suggested, but should do just fine in a morning sun afternoon shade situation. They should flower well there, particularly if it is deciduous shade.

They are not exactly a ground cover plant in my opinion, but if you plant many together or let the seedlings self sow, then they will form a thick mass over time. So, they can be used as ground cover plants, but many people use them as specimen plants as well.

As for invasiveness, I do not consider them particularly invasive, although over time they will form colonies. They are fairly generous with pollen and seed, so each year with decent conditions you are likely to see quite a few seedlings. Since they grow slowly (three years perhaps to blooming size), they are not a significant problem in my opinion; however, I have heard people complain about the number of seedlings.

It also depends on the type of hellebore you grow. In your climate for example, H. foetidus may form colonies rather quickly. In concrete terms, if you were to plant three mature H. foetidus plants in one location, in five or six years the seedlings and resulting plants might cover an area of 50 square feet or so, depending on the conditions.