No. In fact, each poem has a closer relative within the corpus of Keats's work. There's also a stronger connection between "Endymion" and one of Shelley's poems that there is between the former and "Hyperion".
Keats first used the Endymion myth in an 1816 poem, "I stood tip-toe upon a little hill". This poem uses the union of Cynthia and Endymion to symbolize the way in which poets, inspired by natural beauty, write poetry that achieves the status of myth. The longer "Endymion", written the following year, enlarges on this theme by giving the beautiful a moral force. The poem begins:
A thing of beauty is a joy for ever:
Its loveliness increases; it will never
Pass into nothingness; but still will keep
A bower quiet for us, and a sleep
Full of sweet dreams, and health, and quiet breathing.
As long as Endymion pines after the ideal beauty of the moon, it is out of his grasp. But when he falls in love with a mortal woman, she turns out to be Cynthia after all. By enjoying her earthly beauty, Endymion ultimately finds union with his divine beloved after all. The connection with the earlier poem is readily seen, in that the celebration of beauty is granted mythic force as a path to union with the divine.
"Hyperion" is rather darker. Focusing as it does on the Titans after their defeat by the Olympians, it immediately undercuts any sense that to be divine (or to be united with the divine) guarantees that no harm can befall one. Paradoxically, Apollo the Olympian (and the divine poet) becomes a god precisely because he undergoes great suffering and thereby has an insight into human tragedy—something the Titans lack. Keats abandoned this poem, however, around April 1819; perhaps the fact that the Titans are suffering as well made the contrast between Olympians and Titans hard to sustain.
He took up the theme again later that year, in "The Fall of Hyperion". Here too Keats focuses on suffering and the role of the poet. On the one hand, poetry can present false, unreachable ideals to humankind and thus increase its suffering; on the other, poetry can provide a visionary insight into the nature of human suffering and thereby foster compassionate acceptance. Keats ended up abandoning this poem too. It seems that as his views on what poetry should be grew more complex, they resisted explicit expression in any final, resolved form. The shorter "Ode on a Grecian Urn" captures the tensions all the better for leaving them unresolved: the urn, as a beautiful object, is outside human suffering; yet the figures on the urn are also devoid of fulfillment.
It's true, then, that "Endymion" and "Hyperion" share the same mythic universe; Endymion's beloved, Semele (whom Keats calls Cynthia), was in fact Hyperion's daughter. It's also true that thematically, they share concerns: like so much of Keats's work, they are about the nature of poetry and the role of the poet. Yet they are vastly different. The conception of poetry in the later work is darker and less straightforwardly idealistic. There is no evidence that "Hyperion" was intended as a continuation of the earlier work. If anything, the fact that it is in blank verse, as opposed to the heroic couplets of "Endymion", suggests that Keats did not mean to connect the two.
Finally, critics have noted that "Endymion" was influenced by Shelley's 1815 poem "Alastor", and probably intended as a response. "Alastor" tells the story of a poet who, like Endymion, pines after an unattainable lady. Unlike Endymion's, though, Alastor's quest is unsuccessful, largely because he lacks human sympathy. There is an argument to be made that insofar as "The Fall of Hyperion" also take up the theme of poets and human sympathy, it represents a later and more considered meditation on the problems raised Shelley's work. Certainly the two poems have been compared, rather to Shelley's detriment. As far as I know, however, nobody has raised the possibility that Keats was thinking of "Alastor" not just while writing "Endymion", but also some three years later while working on the "Hyperion" poems. If that speculation has merit, then there is another connection between "Endymion" and "Hyperion". Still, they would be connected via Shelley rather than directly with each other.