The symbology certainly admits the interpretation you give it. However, Christianity "borrowed" a lot of its symbols from other traditions (nothing new under the sun...). The son being tied (or glued, in some odd variations) to a tree is older in Norse mythology (I think) than in Christian. In particular, Odin's son is slain at Loki's instigation using an arrow made of mistletoe. The "world tree" is a classic element of Norse mythology: one root in Hell, one in Heaven, one in Earth. One might speculate on the relationships between Christian and Norse symbolism (and many have... ). But since the whole book is framed in terms of Norse mythology, I'm inclined to see it this way.
Which (if you buy any of this ) answers one of your questions... Shadow's real name is Balder.
Which (if you buy any of this ) answers one of your questions... Shadow's real name is Balder.