Kevinsky is correct, you'll need to line them to extend their lives. And they still need drainage. I think using varnish will help in any case, but what I'd do is a little different. I'd plant the plants in other pots, and place them in the wine box, so that it looks like they are growing from the box. This will make the result a lot lighter to lift, as well.
That way, you can use a few bigger plants, or more smaller ones. You can arrange them, and remove individual plants if necessary (say, if one gets a disease). You can also use straw or Spanish moss or something similar to fill in between the pots, making it look like a single planting. That'll also help with stability.
But you will still want it lined, to keep anything damp from remaining in contact with the wood. This will help even varnished wood last longer.
You could also find a close-fitting insert pot, if you want one large pot. Usually, all though it's attractive, wood isn't the ideal pot material. It's a popular style, though, and although there are alternatives, people always seem to want wood. You could make your own wine box from heart redwood (very rot resistant), and varnish that. That would last a long time.