Not only is it possible, but it is "canon!" At the end of the sacking of Troy, Athena caused a fight between the Achaeans that caused them to leave separately on their way home. The old man Nestor, a Troy veteran, narrates it in Odyssey Book 3:

 

αὐτὰρ ἐπεὶ Πριάμοιο πόλιν διεπέρσαμεν αἰπήν,

βῆμεν δ᾽ ἐν νήεσσι, θεὸς δ᾽ ἐσκέδασσεν Ἀχαιούς,

καὶ τότε δὴ Ζεὺς λυγρὸν ἐνὶ φρεσὶ μήδετο νόστον

Ἀργείοις, ἐπεὶ οὔ τι νοήμονες οὐδὲ δίκαιοι

πάντες ἔσαν: τῶ σφεων πολέες κακὸν οἶτον ἐπέσπον

μήνιος ἐξ ὀλοῆς γλαυκώπιδος ὀβριμοπάτρης.

ἥ τ᾽ ἔριν Ἀτρεΐδῃσι μετ᾽ ἀμφοτέροισιν ἔθηκε. (3.130ff)

 

"but when we had sacked the high city of Priam, and had departed in the ships, and the god had scattered the Achaeans, even then Zeus was intending a sorrowful return (nostos νόστον) in his heart for the Argives, since not all were in any way mindful nor just: the wrath of the grey-eyed goddess, the daughter of her mighty father, directed an unhappy fate for two of their houses, and she brought strife for both the sons of Atreus."

 

There were several such tales, but that of Odysseus was the most beloved and most fraught. Originally, there were Greek stories, even epics, about many of them. They are called nostos tales, and the Greek hero characters themselves were nostoi, "home-travelers."

Homer tells us very briefly about the loveable old Greek grandpa Nestor and his very brief nostos in Odyssey book 3: "So we asked the god to give us a sign, and he did, and directed us through the middle of the sea to Euboea, so that we might escape misery most quickly. And a sweet-sounding wind sprang up for us, and the ships ran swiftly over the fish-filled paths, and at night we put in to Geraistos [at the bottom tip of Euboia]. There on the altar of Poseidon we laid many thighs of bulls, thankful to have crossed the great sea. It was the fourth day when the companions of Diomedes, son of Tydeus, tamer of horses, parked their well-balanced ships at Argos; but I held on toward Pylos, and the wind was not once snuffed out from the time when the god first sent it forth to blow."

There are similar little vignettes for other heroes. We hear in abridged fashion how Menelaus lost all his ships at sea and was driven briefly to Egypt, before returning home at last to Sparta. Agamemnon and Locrian Ajax sailed off last from Troy, only to run afoul of weather and lose Ajax. Agamemnon then made it home to Mycenae, but his troubles were only beginning: his wife Clytemnestra had been busy in his absence. We hear (not in Odyssey) that some others decided to walk, and made their way north. Neoptolemos, son of Akhilles, took this path, and had some adventures in Thrace, and even met his famous grandpa Peleus. This was part of a "rival" epic to Odyssey called "The Return of the Atreidai," which traced (in the main) the fates of Menelaus and Agamemnon, but touched on several other nostoi tales as well. It is completely lost, with only a few dubious scraps surviving.

edit: I should add that there is a very very good book on the subject, The Greek Epic Cycle and its Ancient Reception, ed. Fantuzzi (Cambridge 2015).