"Is this passage of scripture the source of the Catholic Church’s teaching against contraception?"
It's the most explicit and therefore easiest to refer to Scripture, so a qualified "yes" is probably the best answer. There are other reasoned arguments but in the age of soundbites and short attention spans they've fallen by the wayside. Most people no longer care enough about their immortal souls to honestly work through a well reasoned argument as opposed to a quick, one line, answer even if the answer is based on something taken out of context.
But you just need to actually let "Scripture interpret Scripture" in good "Sola Scriptura" tradition to arrive at the same conclusion.
Deuteronomy states the penalty for refusing to continue your brothers line and it is definitely not the death penalty. Therefore when Scripture says God killed Odin because of what he did it means just that, not for his intention to not continue his brother's line. So what was it he did as opposed to what he intended? What he did was he spilled his seed on the ground and for what he did God struck him down.
The fact that the contraception supporting crowd who argue over the meaning of Odin being struck dead ignore their own espoused method of interpretation in order to not interfere with their preferred interpretation has long been a source of entertainment for me.
It something of an acid test, actually, of who actually studies Scripture to arrive at the correct interpretation as opposed to saying they have a Scripture based belief when in fact they have just adopted the first lame interpretation that suits their preferences.
Rash, you've got a good point here: grasping the meaning of Gen 38 takes a commitment to a sustained analysis of this chapter itself, and where it fits in with the WHOLE scriptural testimony about God's creative design for human sexuality, lovemaking and marriage, and most people aren't willing or able to do that.
But I would add another point: in the 19-teens and 1920's, Margaret Sanger was launching her Birth Control Revolution together with the other social radicals of her coterie, and Christian churches formed a solid phalanx against her. It was clear she was making war against the decencies of a Christian civilization: she knew it, and they knew it.
But in 1930, the Anglicans gave her the password and the keys to the city when they approved contraception at their 1930 Lambeth conference. They couched it in good enlightened-compassionate-progressive language; and they didn't seem to be fascists, racists and statists like Sanger and her radical friends. They didn't (as far as I know) try to provide a fig-leaf of justification from Scripture at all (which they couldn't, because there are no pro-contraceptive Scriptures): so they just lumped it in with progressive ideals such as the abolition of war and so forth.
By the end of that year, Pope Pius XI came out with an Encyclical letter ("Casti Connubii" -- "Chaste Wedlock") which frontally opposed Lambeth on directly moral and theological grounds and exposed the moral vacuity and theological liberalism of the Anglican position.
However --- as I read it --- at that time, the antagonism between conservative and liberal interpretations of Christianity began to intensify, and basically, in most mainline denominations, the liberals gained the upper hand.
This "Social Gospel progressive" Zeitgeist went entirely for Sanger and the Left, with the American Episcopal church leading the way. Many denominations agreed with Pope Pius as to the moral teaching, but very few spoke out or published any support, perhaps not wanting to side with the Vatican against the liberal "Social Gospel" wing.
That triumphant modernism is, of course, still with us today, but people don't identify it as radical Sanger stuff, they just accept it without much analysis as "the way it is."
At this point, the Sanger radicalism and the Anglican "respectability" have been blenderized into the same mush, and the few voices which still object in the name of God are like "the voice of one crying out in the wilderness."