Yes, that will definitely help, but eventually the wood is going to rot. Don't expect more than a few years out of the flower box. I plan on sealing mine with a product like Kilz, and then lining the bottom with heavy plastic and stapling it to the sides. With some drainage holes. I think...
I've been making notes in my head on how to build a similar little planter for that 3x4x3' extension I have. It wont' last forever, but I plan to make mine with leftover 2x6' and plywood. I'll paint everything with several coats of latex paint, and then line the inside with thick plastic...