Interesting. I think a lot of people find that marriage makes them asexual. ;)
I happen to believe it is possible. In fact I think the Bible says something to this effect also. Something about some men being eunichs because they were made that way.
That's a fascinating observation, and you are exactly correct about the biblical reference to eunuchs from birth:
Matthew 19:12 (King James Version)
"For there are some eunuchs, which were so born from their mother's womb: and there are some eunuchs, which were made eunuchs of men: and there be eunuchs, which have made themselves eunuchs for the kingdom of heaven's sake. He that is able to receive it, let him receive it."