Disclaimer: I'm using a mix of old and new lore to draw my conclusions. We don't really know all that much about the new lore version of Boram. However we know the reason for his downfall was that he strayed away from Noxian ideals.
This entire theory hinders on whether magic is genetically inherited. Yet as far as I would conclude, its not. And Boram wasn't naturally born with the gift of any obvious magic, he had to seek that knowledge but that doesn't mean he could personally practice any of it.
This is an excerpt of Sion's promo:
The elder Darkwill was well versed in the art of necromancy.
This must have required a sort of magical affinity.
Talent for the arcane is a fuzzy thing in new League as for some characters it's innate and inborn (Demacian mages who can barely control it) or acquired later through life (Taliyah). I wouldn't say it's too far-fetched to assume inborn magical talent can be genetic, though it is also possibly that Darkwill's prolonged exposure to magic gave unusual gifts to his children.
Also Noxus isn't a Monarchy, "birthright" probably isnt even a word within their vocabulary. Positions of power is taken by the strong and/or cunning but I can't imagine anyone is first entitled to anything. Plus Noxus is still a bit like a Sovereignty, and I imagine if you lose to any challenge (especially one for rulership), you won't just be humiliated you would be destroyed.
As mentioned before, Darkwill strayed from Noxian ideals. It would not surprise me if he gave his own family too much undeserved privilege and his offspring were almost convinced of their own glorious destiny. This hugely depends on how they write him.
Exactly what happened to Boram... would Vlad really be so naive to repeat his supposedly father's mistakes and not suffer the same consequences as a result?
Again, hugely depends on how they spin it. So far Swain has mostly betrayed and driven away his known allies. I think it will make for a convincing display of his diplomatic ability if he manages to convince the son of his enemy to join him. Two additional points:
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Challenging the most fearsome mage in Noxus and almost besting him despite having less than half his years and experience is a heroic feat. An overly proud leader would kill the foolish lad but a resourceful one would seek to recruit him.
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This is pure headcanon and reliant on old lore, but if hemomancy is so unique and passed down the generations then a strong self-preservation instinct is one of the most important qualities of a blood mage. From the Noxus universe page:
As Noxus expands and defeats neighboring cultures and cities, it offers the conquered people a choice; swear loyalty to Noxus and be judged solely on your worth, or be destroyed.
Someone like Vladimir would definitely choose the former.
EDIT: This is pure speculation of course I cannot even begin to guess Riot's intentions.