Nah, courts wouldn’t let it fly. It’s clearly an attempt to use the civil courts to effectively outlaw what is an unfortunately legal procedure.
It’s not an undisclosed harm. It’s a harm you cannot monetize. How does a P prove that a procedure they asked for caused a specific set of monetarily measurable damages. What other 100 bad things happened in their life?
Additionally, it’s a procedure they asked for, and were required to undergo psychological counseling for before they had the procedure. “I was young and stupid 20 years ago, so I want money now” would not fly.
Also, P was certainly aware of abortion alternatives.
Additional, to hit the final legal point, if I was representing D, I would argue that any damages must be reduced by the amount not spent by the P raising the child. If the abortion created a monetary advantage for the person having the abortion by not having the costs of raising the child, then any award from the abortionist would have to be reduced by the monetary benefit already accrued to the P!
Again, that’s not an issue because the courts would strike it down. The effective judgement from the courts would be, “if you want to attack Roe, fine, but go to the core of the issue, not this BS.”