Let me preface my post with the fact that I am
Pro-Life. To some, this runs counter to many of my positions, I disagree. I think my position on the issue is relevant in the interest of full disclosure.
That said, I read the web page provided, and this has resulted in me planning to run out and get this book, possibly even tonight. I have heard a bit here and there about it, but the guy definitely seems worth reading.
Now,
Is the hypothesis that abortion reduces the crime rate reasonable convincing?Kind of a weakly worded question in my opinion.

However I bet this is an effort to avoid partisan bickering. An effort which is much appreciated.
Is the hypothesis reasonably convincing? Absolutely. I would take it a step further and say that I believe it is more then just convincing, it is likely correct.
Consider the nature of criminals.
Criminals come from all walks of life, but a great many of them come from dysfunctional families. The fail to adequately learn empathy when they are raised in a home where they feel their parents could care less about them. ALso, the often go without corrective action for bad behavior because the parents simply do not care. As a result, dysfunctional families tend to burden society with people who have nearly no understanding of the reality that actions have consequences.
Even more criminals are born out of economic need. When a family is lacking in funds to live comfortably, and a child in inundated with advertising that claims they just can't live without these shoes, or that toy, it is inevitable that a great many of the economically disadvantaged children will turn to crime. How their foray into crime is handled by their parents is a key factor into whether of not they turn into criminals full time. When you combine economic disadvantage with a dysfunctional family you have a recipe that is the most likely to lead to the development of a criminal.
Parental supervision is also key in steering kids away from crime. More criminals come from single parent families than two parent families. This is not because single parents are necessarily bad parents, but because single parents cannot be there for the kids as much. Being there is no partner to help in the raising of the child and the single parent has to work to support the child, these children of single parent families find themselves on their own alot of the time. Lack of supervision frequently leads to bad behavior, and often to crime. Children who successfully experiment with crime are far more likely to become criminals as adults, and unsupervised children are more likely to experiment with crime.
Then there is the issue of children raising children. Most teen parents are not good parents. They have yet to learn how the world works, what their place is in the world, and they have yet learn though experience how to successfully interact with the world around them. It is no wonder that they do a poor job of teaching their children these things when they do not yet understand them, themselves.
For the record, I am not saying that all children of single parent, teen, dysfunctional, or poor families will be criminals, or that the parents is those families are always bad parents. What I am saying is that the majority of these situations lead to these results. There are always exceptions to the rule. Teens who become unusually mature when they become parents, poor families where the parents work tirelessly to push their kids towards a better life, etc, etc.
Now when we look at abortion what do we see. Most abortions happen as a form of post conception birth control. This is irresponsible behavior in my opinion. However, my daughter was born a few years earlier then planned because of my irresponsible behavior and that did not result in an abortion. So, Irresponsible behavior is not the only cause of abortions IMHO.
Many pregnant teens seek abortions, because they are not capable of being parents or simple do not wish to sacrifice their future to raising a child. Many women who simply do not want the responsiblity of a child seek abortions, and many poor women seek abortion because they cannot afford a child. This would suggest to me, that thanks to Roe v. Wade we have a lower crime rate because we have less children being raised in the environments that are more likely to produce those pre-disposed to be criminals.
One argument in opposition to this is the idea that one of the unborn could have grown up to become the person who developed a new way of approaching crime that radically reduced it. Or one of the unborn could have grown up to be the genius that eliminated poverty, etc. This is an interesting point. However the opposite is also true. One of the unborn could have grown up to be a serial killer, crime lord, mass murderer, etc. Considering the demographics of crime and the demographics of abortions I think the latter is slightly more likely to be true.
So I agree with the authors hypothesis that legalized abortion has resulted in lower crime rates. But that begs the question in me of "so what?" I think it is reasonable to suggest that if we changed our laws and began killing everyone convicted of a violent crime of any kind immediately, without an appeal process or long wait, we would probably see a marked reduction in crime. But would that make the killing of these people morally correct? I still have a problem with the morality of Abortion, regardless of the benefit of crime reduction. And I would prefer to deal with the social ills that create criminals then depend on abortion to eliminate the raw material used in their production.
There you go
Erasmussimo, at least one Pro-Life member here sees the hypothesis are reasonable.

Edited to Add:
Doing a bit more thinking and talking on this I thought of something. With our every increasing knowledge of genetics, we learn more and more everyday. If we were to learn that there was a gene or a genetic combination that predisposes someone to violent behavior, would it be moral or just to eliminate those possessing that gene combination before they were born? Personally I do not think so. Who is to say that just because someone is predisposed to violent behavior, that they will not overcome that predisposition? Who is to say that someone cannot be predisposed to violence and still be a benefit to society. Some solutions to our problems are simply not just or moral. Just a thought on my part.