No from me. Why would you consider it? You are setting your kids up to be outsiders who will never fit in. They won't be deliberately excluded but it is a very unusual way to choose to educate your children.
Would you send them to a school where Chinese was the main language because it was a good school? Likely not as they couldnt communicate-they could learn but would never be fluent as they aren't Chinese. This, culturally, is what you are doing. Judaism from my limited experience as a non-Jew (I have worked in a Jewish organisation as a musician) is a complex religion but from what I understand (and please someone correct me if I am wrong- I would hate to offend) Jews are born and die Jewish. It is a race not just a religion. You are a Jew (by birth) or you are not. Your sons are not and never will be Jews. Despite this, they will learn and partake in many wonderful experiences and celebrations and have a fantastic insight into a beautiful culture. It will not be possible to separate however, the culture from their education so they are learning as a Jewish child learns in order to graduate into a Jewish community. Yours will do the same but the culture they will progress into will not be Jewish and so the ways they have learned to think, socialise and behave will exclude them as adults from relationships and opportunities they could have had had they attended a different school.
I think religious schools are a lovely and necessary opportunity for the right child. I think what is more pertinent here however is that a Jewish school offers a safe and culturally supportive place for Jewish children, whose ancestors and elders have experienced horrific abuse from a non-Jewish community within which they were a persecuted minority. It us like someone said upthread, still difficult to be a Jew and anti-sematism still exists in the UK today. So whilst your children may benefit from such a school, they do not need from the school what it offers Jewish children: a space where they can learn and know their religion and their culture, and express themselves and live and learn within their only supportive community. I think from that, that you will find many aspects of the educational journey difficult and I would look elsewhere for your children.
My comments are of course an outsider's view and I think you have had some good asvice from Jewish parents so good luck in whatever you decide.