While Hawthorne and Poe were contemporaries and both wrote in the Dark Romantic tradition, they didn't have a close personal relationship. In fact, Hawthorne was generally critical of Poe's work, finding it overly morbid and sensational.
However, it's possible that Hawthorne read "Dream Within a Dream" and thought about it privately. Without any direct evidence from Hawthorne himself, we can only speculate about his possible thoughts on the poem.
Perhaps he might have found the poem's exploration of dreamlike unreality and the fleeting nature of experience aligned with his own concerns about human perception and the limitations of knowledge. Or, he might have found the poem's focus on despair and disillusionment too bleak and pessimistic.
Ultimately, what Hawthorne thought about "Dream Within a Dream" remains a mystery.