Yes, this is correct.

1. A source for this is Tosfos in Erchin (7a, DH Yashvah), who writes that the reason why the beginning of the Mishnah states that one does not wait for the pregnant woman to give birth is because of Inuy ha'Din. Tosfos writes that Inuy ha'Din applies only after the verdict has been given (Gemar Din). Tosfos implies that before the Gemar Din, since then there is no Inuy ha'Din, one must wait for the mother to give birth.

2. This is also evident from the Rambam (Hilchos Sanhedrin 12:4), who writes that once the Din of the woman has been completed, Beis Din may not delay the punishment to another day, and even if the woman was pregnant Beis Din does not wait until the birth. This teaches that one kills the mother with the fetus only after the trial has been finished; if the trial has not yet started, then Beis Din delays the sentence on the mother until after the birth.

3. It is possible to understand better why Beis Din must wait for the birth if the Din of the mother has not been completed, based on the words of the Meshech Chochmah at the beginning of Parshas Vayakhel. He writes that one is liable for death at the hands of Heaven for the transgression of abortion, because the verse, "And he who strikes a person shall die" (Vayikra 24:21) also applies to killing a fetus. This is also the opinion of Rav Moshe Feinstein zt'l (Igros Moshe CM 2:71, DH Hineh Pashut), who rules that abortions come under the prohibition of murder.

4. According to these opinions, it follows that if there is no prohibition of Inuy ha'Din compelling Beis Din to carry out the verdict immediately, then Beis Din must wait until the mother gives birth in order that they not transgresss the prohibiton of abortion.

Kol Tuv,

Dovid Bloom