Concrete Planter for Euonymus japonicus (Japanese spindle)

You will definitely need to drill drainage holes. Waterlogged soil will kill the plant eventually. I'd be more concerned about the shape of the container. Most pots/planters are either square or circular and transferring it to a different shaped one may cause it to shake/rock in the wind. Difficult to tell how big that planter is though but generally you should move a plant into a new container that is just a little bigger than the previous one.