Shortly put: no, it would not. Let's leave the debate on whether it's the 10th or the 13th century we're talking about for a bit, but focus on the elements of the story. This particular episode, and a number of others set in Egil's youth, have the function to introduce the character of the protagonist. In this sense, this episode is used to illustrate Egil's eagerness to use extreme violence and start feuds, regardless of the longer-term consequences of his actions. Egil is not an ideal hero. I can not think of any perfect modern analogues to his character, though antiheroes like Billy the Kid, Al Capone or Hannibal Lecter approach the trope.

In any case, within the saga Egil's violence is described as being encouraged by his tutor (the most significant shaping force for Icelandic aristocratic youths, who had a tutelage/clientage exchange programme with other allied aristocrats), praised by his mother, but ignored by his father. Basically, what all these characters are saying is that violence is a good characteristic of the proper aristocrat, and that Egil's display of violence at such a young age shows his maturity. Of course, for the audience there would have been a disconnect, and they would certainly have recognised this as 'bad parenting'. What the adults are ignoring is that Egil's actions have consequences. This happens a few months later, when Egil is almost killed by his enraged/berserk father, and when he himself takes revenge on his father's dependents.

So what would be uncharacteristic in Egil's behaviour is that he behaves as an independent aristocrat already at such a young age, instead of being a client of his patrons (his tutor and parents). This makes his behaviour erratic and childlike, which means he never learns the difference between 'proper' and 'just' violence, and his quick rage. This is because his father, an unreliable and monstrous berserk, is not taking his proper responsibility.

Egil's saga is fairly well studied, but a good discussion of Icelandic youth and violence and an analysis of the saga from a literary and psychological perspective can be found in Troublesome Children in the Sagas of the Icelanders,“ Saga-Book 27 (2003), 5–24. Further reading on the different status of violence in Viking society can be found with Guy Halsall in 'Violence and society in the early medieval west: An introductory survey.' Violence and Society in the Early Medieval West, ed. Halsall, pp. 1-45., or 'Playing by whose rules? A further look at Viking atrocity in the ninth century.' Medieval History vol.2, no.2 (1992), pp. 3-12. Some earlier examples are discussed in [Newbold's Interpersonal Violence in Gregory of Tours’ Libri Historiarum] (http://www.brepolsonline.net/doi/abs/10.1484/J.NMS.3.226?journalCode=nms), or a more sociological/psychological general perspective in (Rosenwein's Anger's Past)[https://books.google.dk/books?id=XgPXeJCPhr0C&hl=nl&source=gbs_navlinks_s].