Using the Heidelberg Catechism again as a reference, I believe that both groups can and are addressed in the following Questions and Answers.
Q. 81 Who are those who may come to the
Those who are TRULY DISPLEASED WITH THEIR SINS and TRUST that they are forgiven them(newly converted)and that their remaining weakness is covered by the suffering and death of Christ. And who also desire more and more to strengthen their faith and amend their life(confessing).
But hypocrites and those who do not repent eat and drink judgment to themselves.(both newly converted and confessing-SEE Admonitions Against Eating Unworthily).
The catechism is clear that those who are displeased with their sins are to be admitted to the Table. It does not qualify whether or not these people should be confessing members or not nor does it dictate an age.
The second part of the answer actually could apply to both the newly converted and those who have attended regularly.
It can be argued, of course, that as children and youth the participants will not fully understand what it means to be strengthened or the full ramifications of trusting in Christ. However, the same argument can be applied to adults who have already confessed their faith.