No. But what happens will depend on the age of the child.
Where the child is below seven-years-old, and will go on to have a Jewish upbringing and education, they are regarded as Jewish without need of conversion. The Liberal Beit Din (Rabbinic Board) will issue a status certificate, if required.
Where the child is over seven, Liberal Judaism would recommend attendance at religion school leading to bar/batmitzvah and Kabbalat Torah, at which point the child is considered fully Jewish. Again, a status certificate will be issued if required.