In a recent moment of clear speech, one of the leading proponents of paedocommunion, James Jordan, says no. Here are several clear statements from Jordan:
I’ve said for years that paedocommunion and non-pc cannot live together any more than infant and adult baptism. And by returning to pc, we drive back 1000 years, and definitely back before the Reformation.
Oh, it’s true enough: We depart from the whole Reformation tradition at certain pretty basic points. It’s no good pretending otherwise. I think the PCA is perfectly within its rights to say no to all [Biblical Horizons] types. We are NOT traditional presbyterians. The PCA suffers us within itself, but we are poison to traditional presbyterianism. We are new wine, and the PCA is an old skin. So, for the sake of the people we are called to minister to, we do our best. But we don’t really “belong” there.
I can’t really put feet on this, but I “feel” sure that the Reformation tradition is rationalistic precisely because it is anti-pc. Or maybe better, these are part of one complex. Being anti-pc was the greatest mistake of all the Reformers (except Musculus, and who cares about him?). This mistake is part of the heart of the Reformation; they knew about pc and rejected it.
But there’s no reason why the presbys should receive us, since sacramentally speaking we are NOT Reformed and NOT presbyterian.
I’m a little bit sympathetic with Duncan & Co. when they suspect some of you guys are not being honest when you try to show that you’re just good traditional Reformed guys. I guess it’s a good thing I did not make it to the Knox Seminary discussion, because I would have openly said, “I’m not on the same page as Calvin and the Reformation in these regards.” Showing that the Reformed tradition is wider and muddier than Duncan wants it to be is fine, but the fact is that if you believe in pc, you’re not in the Reformed tradition at all in a very significant and profound sense. No more than you’re Baptists.
I don't think it gets more clear than that.