We need to be careful with this question, as nowhere in "Calamus" does Whitman imagine having a conversation with Homer or Virgil. However, what you can definitely see is the way in which Whitman takes the ideal of male love--romantic or otherwise--that is espoused in texts such as the epic classics by these two authors and carries them on into his own context, discussing in particular concepts such as "comradeship." If we think about the relationship between Achilles and Patroclus in The Iliad, which most recently was explored in all of its homosexual intensity in the Orange prize-winning The Shield of Achilles, the concept of the bonds of affection that draw men to each other are definitely raised in such texts.
If we look at some of the poems in "Calamus," we can therefore see that Whitman draws on such ideas and develops them, exploring them in his own context. Consider the following lines of the third poem in the "Calamus" sequence:
Or possibly with you sailing at sea, or on the beach of the sea, or some quiet island,
Here to put your lips upon mine I permit you,
With the comrade's long-dwelling kiss, or the new husband's kiss,
For I am the new husband, and I am the comrade.
The deep and close relationship that can form between two men fighting alongside each other is therefore explicitly addressed, with phrases such as "the new husband" and "new husband's kiss" overtly suggesting a strong and physical sexual relationship. Such references clearly show how Whitman takes the ideas of male-male love in the words of Homer and Virgil and carries them on into his own time.