Can the 5e Staff of the Woodlands (magic item) be subject to an Awaken (spell)?

A Staff of the Woodlands can take the form of a healthy tree (60 feet tall / 5-foot-diameter trunk / branches spread 20-foot radius).

The Awaken spell can give sentience to a tree, turning this item into an Awakened Tree. This would make a really nifty, helpful and interesting magic item for players – and also turn it into an NPC, controlled by the DM in about 30 days time. Win-win.

Would this work – or does the pre-existing magic in the tree-version of the staff repel this spell?