No, this would have been unnecessary. Matthew's Gospel preceded both Luke & Marcion, and Matthew's Gospel contains a birth narrative. If Matthew is the standard by which future Gospels were judged (and it was the standard as early as the writings of Papias--see HE 3.39), then it is Marcion, not Luke, who was reacting to a competing form of Gospel.
Chronology of Matthew vs. Marcion
Matthew is quoted by Ignatius & Polycarp, writing circa AD 107. Edouard Massaux argued effectively that Matthew is also quoted in 1 Clement (written late 1st century), given exact correspondence in unusual Greek wording. (see pp. 21-24 here) Matthew is also quoted by the Didache, which appears to have been written well before Marcion, and may even date to the mid-first century. A passage from Matthew is found in the Epistle of Barnabas; the date of this epistle is uncertain, but Robinson (Redating the New Testament Ch. 10) makes a compelling argument that it was written in the 1st Century.
Marcion's Gospel doesn't show up until well into the 2nd century--even a very late date for Matthew puts Matthew chronologically ahead of Marcion.
Chronology of Matthew vs. Luke
All of the currently most popular solutions to the Synoptic Problem and all of the Patristic writers who discussed the subject, agree that Matthew was written prior to Luke.
Additionally, the fact that the early, Gentile-dominated church used Matthew much more than they used Luke becomes very difficult to explain if Luke preceded Matthew. The Jewish Gospel of Matthew (which refers to Gentiles as dogs) had little chance of upstaging the Gentile Gospel of Luke in a Gentile-dominated church (at a time when Christianity & Judaism were bitterly separating) if Luke was in circulation prior to Matthew. The clearest explanation for why the Gentile church treated Matthew as the primary source is that it was the primary source.
I discuss this further in this series on my channel: Who When & Why - the Writing of the Gospels.
Chronology of Luke vs. Marcion
The Gospel of Luke is quoted by Polycarp (writing circa AD 107). Polycarp of Smyrna was a disciple of the Apostle John and one of the pillars of early Christianity. Although there are many good reasons for dating the Gospel of Luke well before this time, even this extremely cautious estimate puts the composition of Luke (and only one version of one Gospel is attributed by the early historians to Luke) at a time when Marcion was but a very young man.
References to Marcion's work don't show up until a generation later. Polycarp & his pupil Irenaeus vehemently rejected Marcion as a fraud. Marcion's contemporaries were in a position to fact-check Marcion and they rejected him--Justin Martyr is a great example.
If there were multiple versions of Luke circulating, or Luke were based upon the writings of Marcion, Justin was in a position to know. That Justin relied upon Luke as an authentic, apostolic, non-Marcionite source--when his life was on the line presenting apologies to Rome--is very good reason to believe that Luke is neither in whole nor in part a result of the work of Marcion.
Marcion's Gospel was a response to prior, existing sources, including Matthew & Luke, not the other way around.