Probably, depending on how the Clanners in power try to get around their own laws. Consider the fact that the one freeborn we know of who won a Bloodname actually did so in perhaps the most restrictive of Clans when it comes to such things (Clan Jade Falcon). AND said warrior was the offspring of another warrior who spent his entire life violating Clan laws.
At the end of the day, it's your gaming table. Feel free to do whatever you like at it.
- Herbert Beas