At the birth of Jesus, the chorus of angels are singing peace and when Jesus makes his triumphal entry into Jerusalem riding on a donkey the chorus is singing “Blessed is the king that cometh in the name of the Lord. Peace in heaven and glory in the highest!” This was a different kind of victory procession. A humble king riding on a donkey with an army carrying psalms is not a threat to Pax Romana.
Luke's preoccupation with peace is certainly a noteworthy observation, but the conjecture that "[a] humble king riding on a donkey with an army carrying psalms is not a threat to Pax Romana," with its implicit corollary that Roman provincial officials would have been willing or able to differentiate between the peaceful demonstrations of a jubilant crowd and the zealous declarations of a nationalistic mob, seems somewhat dubious. Josephus' account of the swift execution of the messianic pretender Theudas and many of his followers after their symbolic journey to the Jordan (Antiq. 20.97-28) suggests that almost any large gathering whose actions could be viewed in an incendiary or revolutionary context was subject to reprisal. Whether the triumphal entry was intended to be such a gathering is an open question, but it seems likely that the authorities would have viewed it as such--at least if it were as dramatic as the gospels suggest.
It might also be noted that the Lukan Jesus flatly denies that he comes bearing earthly peace on at least one occasion: "Do you think that I have come to bring peace to the earth? No, I tell you, but rather division!" (δοκεῖτε ὅτι εἰρήνην παρεγενόμην δοῦναι ἐν τῇ γῇ; οὐχί, λέγω ὑμῖν, ἀλλ᾿ ἢ διαμερισμόν; Luke 12:51, the parallel of the Matthean Jesus' promise that "I have not come to bring peace, but a sword").