Yes, Hanna (in Fargo) it's true — some female wood-warblers sing.
Your question relates to the larger question of how singing birds develop their song.
Next, note that wood-warblers are like most other songbirds. They experience a period of practicing a song in a stage that is called "plasticity."
Depending on the species of wood-warbler, true, definitive adult song is achieved by no later than the commencement of the following breeding season after a newborn singer arrives in a previous year's brood.
When that moment of virtuosity appears, it's called "crystalization" (when complete, full, learned song can be repeated by an individual).
Now there's a magnificent term that rings a chord of delight in any birder's heart.
Meanwhile, I'm Ready, Set, Go for the spring migration north of the wood-warblers? Are you?