Not really. If I recall, legalizing abortion has almost no effect on the birth rate, accessible contraceptives are somewhat higher, but none come close to changing cultural norms.

Well, this is what I found in < 5 minutes of searching:

...Klerman finds that legalization of abortion, particularly the broad access afforded by Roe, had some effect in reducing fertility.

-- Klerman, Jacob Alex. "US abortion policy and fertility." (2000).

I find fairly strong evidence that young women’s birthrates dropped as a result of abortion access as well as evidence that birth control pill access led to a drop in birthrates among whites.

-- Guldi, Melanie. "Fertility effects of abortion and birth control pill access for minors." Demography 45, no. 4 (2008): 817-827.

Our model estimates women ages 14 to 19 will see an 8.7% decline in birth rates, a 4.1% decline for women ages 20 to 24 and a 3% decline for women ages 25 to 29 due to abortion legalization. We predict that abortion legalization is correlated with a 10.2% decrease in the birth rates of black mothers and a 4.5% decrease in the birth rates of white mothers.

-- Coates, Brandi, Alejandro Companioni, and Zachary A. Bethune. "The Impact of Abortion Legalization on Birth Rates!."

Okay, so a quick search for studies on the effects of abortion legalization on birth rates seems to confirm my priors, so...it still looks like an extraordinary claim.

50 million mostly legal abortions, even if the figure is correct, does not translate to 50 million more adults, of course.

Agreed, I shouldn't have used that number, but according the first couple of studies I came across it definitely would be positive and over 40 years time it seems plausible that even some of those people that would have been born would have had kids by this point.