Doesn't seem likely. When you look at a variety of Europe countries which have a variety of different dates when it comes to loosing / strengthening abortion laws they also saw decreases in crime in the same time period as the US.
People who decide to get kids will always be more likely to do so when they can actually support them.
People who get kids by accident (or even against their will) will be more likely to put kids into unstable environments.
Kids in unstable environments are more likely to grow into adults that do crime.
One way of avoiding these kids is abortions. But you could also provide stable environments for kids that are actually born (which is very much what we in Europe did). Allowing abortions won't change a lot in a society that already does what it can to support all children and their parents — it however will change a lot in societies without social security.
I am not saying abortion doesn't have an impact, but Roe vs Wade did not. There were a lot of abortions prior to the legalization in the US. I am not positive, but it may have been legal in some states just not nationally (didn't want to look it up to confirm).
This is why the date of legalization of abortion did not seem to have an impact in Europe and also why restrictions on abortion in some countries did not have an impact.
> documented abortions rose sharply in the wake of Roe, from under 750,000 in 1973 (when live births totaled 3.1 million) to over 1.6 million in 1980 (when live births totaled 3.6 million). If illegal abortions were already being performed in equivalent numbers, one would not expect a seven-year lag in reaching a steady state. Moreover, the costs of an abortion — financial and otherwise —dropped considerably after legalization.
You are correct some states were legal earlier. Donohue and Levitt have a section on that in a 2019 follow up paper [2]. Claim: Crime dropped earlier in those states that legalized earlier.
[1] http://pricetheory.uchicago.edu/levitt/Papers/DonohueLevittT...
[2] https://bfi.uchicago.edu/wp-content/uploads/BFI_WP_201975.pd...
This is why the date of legalization of abortion did not seem to have an impact in Europe and also why restrictions on abortion in some countries did not have an impact.