TLDR: the hypothalamus is involved in fear processing, but not in the way you think.
Wikipedia has a decently sourced article on the hypothalamus and it does play some role in fear processing:
The medial zone of hypothalamus is part of a circuitry that controls motivated behaviors, like defensive behaviors. Analyses of Fos-labeling showed that a series of nuclei in the "behavioral control column" is important in regulating the expression of innate and conditioned defensive behaviors.
Antipredatory defensive behavior
Exposure to a predator (such as a cat) elicits defensive behaviors in laboratory rodents, even when the animal has never been exposed to a cat. In the hypothalamus, this exposure causes an increase in Fos-labeled cells in the anterior hypothalamic nucleus, the dorsomedial part of the ventromedial nucleus, and in the ventrolateral part of the premammillary nucleus (PMDvl). The premammillary nucleus has an important role in expression of defensive behaviors towards a predator, since lesions in this nucleus abolish defensive behaviors, like freezing and flight. The PMD does not modulate defensive behavior in other situations, as lesions of this nucleus had minimal effects on post-shock freezing scores. The PMD has important connections to the dorsal periaqueductal gray, an important structure in fear expression. In addition, animals display risk assessment behaviors to the environment previously associated with the cat. Fos-labeled cell analysis showed that the PMDvl is the most activated structure in the hypothalamus, and inactivation with muscimol prior to exposure to the context abolishes the defensive behavior. Therefore, the hypothalamus, mainly the PMDvl, has an important role in expression of innate and conditioned defensive behaviors to a predator.
Likewise, the hypothalamus has a role in social defeat: Nuclei in medial zone are also mobilized during an encounter with an aggressive conspecific. The defeated animal has an increase in Fos levels in sexually dimorphic structures, such as the medial pre-optic nucleus, the ventrolateral part of ventromedial nucleus, and the ventral premammilary nucleus. Such structures are important in other social behaviors, such as sexual and aggressive behaviors. Moreover, the premammillary nucleus also is mobilized, the dorsomedial part but not the ventrolateral part. Lesions in this nucleus abolish passive defensive behavior, like freezing and the "on-the-back" posture.
Just based on that it's easy overemphasize the importance of the hypothalamus in fear processing; it's actually not that central. If you want the popsci version, then the amygdala gets the center stage in regulating fear. From a review of the "Neuronal circuits for fear and anxiety":
I don't see why the homeostasis circuitry would be involved in fear processing (as you propose), and as far as I can tell, it isn't.