Answer: In order to bloom their best, rhododendrons actually prefer some sunlight, either direct sun during the morning or a dappled bright light all day. If the tree has been limbed up, there may be ample light there for it to bloom. If not, rhododendrons are fairly easy to transplant since they are shallow rooted.
On the other hand, I suppose it is possible that a heavy crop of larger hickory nuts raining down could possibly mar the foliage. I have not personally grown one under a hickory tree, but I know that acorns are not heavy enough to damage them, they seem to bounce and roll right off. Again, you could try it and see.
The other consideration is to make sure the tree does not outcompete the rhododendron for moisture, either by roots or by shedding it via the canopy.
I am sure you will enjoy this rhodie wherever you decide to place it, the color is fabulous.
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