Whilst it might "work", you will definitely not get full usage out of the R9 380 or the GTX 960 for that matter. As said above, a minimum of 500W is required. Sure, it might run the card, but performance in games will be pretty bad as not enough power will be supplied to the card, and therefore the GPU load won't go above a certain amount (50% in most cases) If you're going to spend the money to gt a nice GPU, just throw a little extra in and upgrade to a high quality power supply. Afterall, what's the point in buying a nice new card if there's a chance the power supply could destroy it?
Hope all goes well with your decision.