There were plenty of religious references in halo, but I do not think it was Bungie's intent to make the connections you did in Destiny. For example, what connections does the Traveler have with God the Father? Just that he saved the people in the last city? Wouldn't he be better related to Jesus? But even if you relate him to Jesus you must take into account that the Traveler was defeated and used its last effort to save humanity. After Jesus 'saved' humanity, he ascended into heaven (according to the Bible).
Also, aren't the Holy Ghost, Jesus, and God the Father interconnected? Sure, Ghost speaker and traveler are connected in some way, but their not the same personality.
And why is the speaker Jesus? There is no connection I can see.
tl;dr,
There's too many inconsistencies between Destiny and Biblical lore for the connections you presented to be intentional.