Miraculously, I have a batch of BW in my basement getting ready for bottles right now brewed in exactly the fashion I described. It's the second batch I've brewed doing it just this way, and they are both most certainly sour.
On Deck: Saison "Jardin d'été" (3rd Gen 3711, Wild bugs, Pale ale malt, wheat, Willamette dry hop)
Primary: Saison "Vomissure de Grenouille" (2nd Gen 3711 from dregs, Pale Ale malt, Crystals and Willamettes)
Secondary: BM45/Spontaneous Bugs Experiment (down to 1.004, and tastes awesome), contemplating what fruit to add.