I'm not a dr by any means, but I can share what I've gleaned from a bunch of internet research. Family history can increase the likelihood of hypothyroidism, especially when the relatives affected are on the maternal side. My maternal aunt and grandmother both have thyroid disorders. (I'm not sure if they are hypo or hyper.) However, my mom has never been diagnosed and doesn't have symptoms.
So I would assume it likely to increase the child's risk of having hypothyroidism. I am not sure when the majority of folks are diagnosed. I personally was not diagnosed until I was 26. My symptoms weren't evident until I was in college. The quality of my childhood was just like any other kid and completely unaffected by the hypothyroidism. Elduderino might be able to expand more on this than I can.
As far as affecting the viability of your sister's eggs when donated to you, you will have to ask the endocrinologist and your ob/gyn/fertility specialist. My understanding of pregnancy difficulties due to hypothyroidism is that they arise due to the mother being hypothyroid. Assuming that you aren't hypothyroid, I wouldn't think that you would have trouble conceiving due to the hypothyroidism.
We had my levels regulated within 3 months of starting my meds, and I was preggers within 4 months.
I've followed your struggle with infertility as well as luckylily's. I truly hope and pray you will join us on the pregger side soon.
And Hawaiian, thanks for the congrats!