Does "A Poison Tree" by William Blake suggest that because people enjoy being angry they tend to want to nourish their hatred rather than overcome...

This is a very subjective question which requires a
subjective answer. What this means is that every reader interprets a text, especially
poetry, in different ways.

As for the poem "A Poison Tree",
one could textually justify that anger is easier to nourish than
overcome.

This theology is compounded by the image of the
tree. It could remind one of the Biblical saying from Luke
6:43:

No good
tree bears bad fruit, nor does a bad tree bear good
fruit.

Therefore, a tree
rooted in wrath will bear nothing but wrath. Regardless of how adamant a person is,
wrath is something which can become so deep-seeded that a simple 'watering' of fears
will not insure that wrath will simply go away.

Therefore,
the fact that the speaker is glad to see his foe dead at the base of the tree speaks to
the fact that wrath is more deeply rooted in man than one could
imagine.