Lynn, your last post made me grin happily. So glad you like it here.
I agree with others that think you should be fine using this area for additional shade plants. Just keep in mind that the tree will draw all the available water it needs from this area, regardless of the needs of your smaller plants. Just try to pick a time for planting out when there's likely to be plenty of supply and less of demand. Now would be a good time in our area for planting out many perennials. Mulching after the ground freezes so that it stays frozen all winter long helps too. Have some on hand and store it dry if possible so that it doesn't freeze into unworkable chunks. I usually just cover my leaf pile with a tarp. Lower areas will sometimes freeze, but the top and sides of the pile are generally usable all winter long.
As for additional plants for dry shade, you might look into some of these...just a few of the many choices available.
Hakone grass, heuchera and others
http://garden.org/apps/sets/vi...
Lily-of-the-valley
American Lily of the Valley (Convallaria majalis var. montana)
Foam Flower
http://garden.org/plants/searc...
Jack-in-the-Pulpit
http://garden.org/plants/searc...
Anemone blanda planted in tree roots returns for me every spring; regardless if it gets any summer irrigation, or not.
Grecian Windflower (Anemone blanda)
Colorful pots of annuals like mimulus, impatiens and begonias set uphill of new transplants will provide extra moisture for the ones in the ground below; provided of course, that you'd want to water them all season long.