I don't think so. Unless someone can come up with a legit explanation for how this could happen, I don't buy this for a second. Yakone's declaration of coming from the most powerful line of Bloodbenders never made sense to me.

Then again, I have many problems with Tarrlok's flashback.

i think it would make sense if they were related

I think it's definitely a feasible theory, especially because we don't know of any other Bloodbenders in the Avatar world, except for Katara, who was disgusted by the ability. Mike and Bryan would certainly incorporate an interesting connection like this between the two series, so I wouldn't be surprised at all if the Yakone family line descended from Hama.
The quote by Hama at the end of The Puppetmaster especially provides some substantial evidence, when she says, "My work is done." She is implying that she has successfully planted the seed in another Waterbender and has passed on the ability of Bloodbending, even if her pupil doesn't entirely agree with it. What really bothered me was when Katara used Bloodbending later in The Southern Raiders. It just seemed completely inconsistent with her character, despite how upset or angry she may have been. But this is a completely separate discussion, and I don't want to get off topic.

Hama couldn't have kids because she was old. She was from the Southern Water Tribe while Yakone and his sons were from the Northen Water Tribe. If Hama taught Yakone and other waterbenders bloodbending, why Tarrlokk didn't mention it to Korra? And why Aang didn't warn her about it too?

Personally, I think that the fact that Hama seemed to feel her "deed was done" when she taught Katara bloodbending shows that she was in the buisness of teaching people. Personally, I believe one of her pupils, other than Katara, learned it, perfected it, and taught it to his children. Honestly, the ages do not really add up that well to Hama being the mother, unless you believe she got pregnant at 50 which I find highly unlikely. And there is no evidence that says that Hama had not taught anyone else bloodbending. However, there are clues that point to the fact that she would be willing to train others in the art. Also. I feel that by saying you came from "the most powerful line of bloodbenders" it shows that there were other bloodbenders than Hama and Katara. LIke, Katara refused to use bloodbending and would never teach anyone and if these were the descendants of Hama then there would only be one line of bloodbenders, so I don't see the need to reiterate that they are the most powerful line of bloodbenders. To me, this shows that she had multiple pupils or one pupil that trained multiple people and then it became a family thing. And lastly, Hama and Katara could only blood bend during the full moon. Therefore, someone would have had to change the technique to be able to blood bend at will. That being said, I do not believe this technique was changed from one of Hama's offspring because it is implied, not stated, that Yacone and his children gained this ability from a strong genetic aptitude at bloodbending. So, I would say this gives evidence to the fact that one of Hama's pupils was just more skilled at bloodbending than her and carried a gene that was highly attuned to bloodbending. It begs the question, if this is a genetic ability, why would she not posses it but all of her descendants would? I understand that many might say that Hama had the genetic capability but did not develope the talent. However, we have to give Hama some credit. She invented bloodbending, which means she is one of the best bloodbenders to have ever existed. So, you have to figure that she must have tried bloodbending at times other than the full moon if she were trying to escape prison. Also, she probably would have accomplised it, if it were possible for her. She had the motivation, so if she had the ability to she probably would have. Many might try to say though that she had the ability but did not develop the skill just as Amon developed the ability to take away others bending. Assuming that he was her descendant, this would prove that more advanced abilities requiring more skill could develop from her children. However, she did not want to take away people's bending, so this does not show whether she did not posses all the abilities that her children did because she would never attempt to remove someone's bending. Yet, she would try to bend when the moon was not full because she didn't really know what she was doing with bloodbending at first and it is unlikely that she only attempted this during full moons. Rather, though one could argue against this I find it more likely, she would have tried to blood bend on several occasions and realized that she was not really able to except during full moons. She practiced bloodbending regularly, so I find it highly likely she would attempt to bloodbend when the moon is not full at some point, at least out of pure frustration at her limitations if not out of desperation to try to escape more quickly. None of these evidences prove that Yacone and his children did not descend from Hama, but I believe they show there is a stronger case that they did not.

So, your response is that you'll respond?