By the pledge itself, do you mean the 'under God' portion?
Yes.
As far as the establishment clause is concerned, there is no difference between declaring that God exists, and declaring that Jesus Christ is the Son of God. Both are religious affirmations, which Congress is forbidden from making.
I can't support a conclusion that it's OK for the States and not for the Federal government to have a brief "under God" in the pledge...
Why not? The establishment clause, like the Tenth Amendment, is a federalism provision, and is therefore incapable of being incorporated.