according to the general Talmudic understanding of this Name, it derives from "Strong" and generally means "Protector", similar to the Arabic word "Shahdah", having the general meaning of "closed" and "shield". Right in line with this explanation, the Talmud tells us that Shadai is an acronym of {Shomer Taldot Yisrael} - the Guardian of the Doors of Israel. In fact, this is the Name inscribed on the outside of the Mezuza parchment scroll.

There are, of course, plenty of sources in Scripture that also support your interpretation. Except for one important thing. It's not that G-d is called "my boobs", but rather that both G-d and Breasts are called that because they are both the source of "nourishment" and nurturing. It's a side by side semantic relationship, not one deriving from the other.