I don't really see how the German wording points in that direction. Can you demonstrate what you are going by in the German to connect the two? In English "I am" can, because "I am" is how God's name is translated in Exodus 3:14. But the German wording in the poem doesn't seem to match the biblical wording at all.
But the suggestion that Mary now feels eternal means that in a small way she is sharing in God's being
Not sure about that. It is hard to imagine Mary playing with God's name that way - using it to refer to herself or liken herself to God. It seems a devout Jewess of those days would be more likely to consider it as bordering on blasphemous, and therefore not something she would be willing to do.