Could Penelope be related to the repeated line "rose fingered dawn" in the Odyssey?

Although there is one use of "rosy-fingered dawn" that relates directly to Odysseus and Penelope, which I will discuss briefly below, it is unlikely that the phrase "rose-fingered dawn" (and all its variations) can be identified with Penelope.

In Homeric epics like The Iliad and The Odyssey, the poet uses phrases known as epithets which, when they refer to gods or certain men, usually great warriors, become a formulaic reference.  "Rosy-fingered dawn," for example,...

Although there is one use of "rosy-fingered dawn" that relates directly to Odysseus and Penelope, which I will discuss briefly below, it is unlikely that the phrase "rose-fingered dawn" (and all its variations) can be identified with Penelope.

In Homeric epics like The Iliad and The Odyssey, the poet uses phrases known as epithets which, when they refer to gods or certain men, usually great warriors, become a formulaic reference.  "Rosy-fingered dawn," for example, is used many times in Homeric and classical literature to refer to the goddess Eos (also, Aurora, Dawn), who brings the first light of day, usually red or rosy, from the East.  If we were to count the number of times this epithet for Eos is used in The Iliad or The Odyssey, we would probably discover no significant difference.  More importantly, classical writers after Homer used the same epithet many times, including Virgil in the Aeniad.  Similar epithets include phrases like "the grey-eyed goddess Athena" (also, "blue-eyed"), "swift-footed Achilles," and "father of us, sovereign above all rulers," a very common reference to Zeus in The Odyssey. Epithets are rhetorical devices in that they take an abstraction--dawn, for example--and make the abstraction a concrete image, something that everyone can understand.  Homeric epithets may have developed from earlier poetic traditions for Greek mythological figures, and they may have developed as part of oral literature in order to help the poet, who relied on memory to recite hundreds of lines, recall the beginnings of important sections.

Your question about Dawn and Penelope may arise from a section of Book 23 in which Athena brings about the dawn after Odysseus and Penelope have been able to make love and sleep after Odysseus has gotten rid of the suitors:

When [Athena] felt that Odysseus had taken his full pleasure/in making love with his wife and sleeping beside her [Penelope],/she permitted Dawn to leave the river of Ocean/and bring the first light to mankind.

What is important here is that Athena, not Dawn, is in control of the action.  Odysseus and his family are still in jeopardy, and Athena continues to guide them as they try to find a way to satisfy all the relatives of the slain suitors.  In this scene, as in other appearances, Dawn fulfills an important function based on her Homeric significance as an epithet.