I'd say it would have had similar effects like the OTL sexual revolution. And I don't even think that oral contraception changed sexual mores instantly, I rather think that society just had been "mature" for oral contraception, just as the world was mature for Gutenberg's print press because there were so many texts waiting for printing and publication, readily fuling the end of the Medieval Era. But it's nice to speculate WI oral contraception had been invented in the Muslim world, and WI it wasn't in 20th but rather in 10th century or so.
All demographic data say that the easy access to contraception is highly important for low fertility, while easy access to abortion isn't or at least isn't that important, except for countries like Russia where two abortions come up for each birth. A good example is to compare Irland and Poland. Irland gradually legalized contraception and the poor Ireland rushed into the demographic window making the "Celtic Tiger" possible. An Irish solution for an Irish problem. Abortion is still illegal in many ways, but this couldn't change the trend and would never do. Poland must have always had standard European mores in contraception access and between 1956 and 1993 abortion was largely legal before the Church reached to get more restrictive abortion laws passed. Though abortion is a real problem in Poland, it is one of the least fertile countries right now (1.25 children/women) and had been at healthy 2.0 children/women before the Autumn of Nations and its economic crackdown. And remember, until that crackdown, Poles had easier access to abortion than today.
I may even remind that France and Scandinavia had really serious fertility crisises in the Interbellum, esp. during the Great Depression, and their were no real access to modern methods at all. After the war, and some 15 to 20 years before the widespread use of oral contraception, de Gaulle forced France to "bear 12 million children" which happened until about 1960. And the fertility of the French and the Scandinavians is still higher and nearer to the healthy 2.0-2.2 childern/women than in other European countries.
Answering the final question, the Baby Boom of the late 1940's still would have occured because it was largely the result of WWII. Nobody really likes to conceive children when there is the danger that the father might die in the battlefield and the child raises up as a half-orphan. People waited until the war was over (just as e. g. GWB's parents did) and then made the babies they had made two years earlier if war never occured.
Maybe the boom would be a bit smaller, but just a bit.