I would just use those as cachepots with another pot inside them (something like those black plastic round containers shrubs come in would work well, if they will fit). You would need a tray or bowl in the bottom to catch the excess water. It seems like they would get really hot if they'll be in full sun, but I've seen plants growing in old iron cooking kettles, so I guess it might be ok. The plants I've seen growing in iron kettles were always things like portulaca or hens and chicks with shallow roots. Sweet potato vines will need better drainage than that, so you wouldn't want to plant them directly in those pots.

I agree with Julie's suggestion. It would work best to have the plants in a separate plastic pot inside your copper pots with the plastic pot sitting in a saucer also located inside the copper pot. Otherwise, any plants in those pots could drown quite easily. A layer of rocks does nothing to prevent the plants from drowing in a pot that does not have drainage holes.

You may or may not have issues with the heat cooking the roots of the plants. I use some galvanized metal containers outside my barn and potting shed and they and their soil can get really hot in summer. I work around that by planting trailing plants that shade the sides of the planters or by arranging plants in smaller plastic pots around the metal ones so the plastic pots can help shade the exterior of the metal containers. I also place most of the metal containers where they get morning sun and afternoon shade.

With your plastic pots inside the metal pots, it will be easy to lift out your plastic pot containing the plant, lift the saucer out and drain off the water, etc. In weather like we're having right now, you'd have to do this every day or two, and certainly following every rainfall.

All my metal containers have holes drilled in them for drainage. It just makes life simpler if I don't have to worry about the plants drowning in their containers.

I have grown ornamental sweet potatoes in those metal pots many times, but only in the larger containers so they won't become rootbound. By large, I mean really large--from 10 gallon to 200 gallon. There are other trailing plants you could put in your copper pots if they are not large enough for ornamental sweet potatoes---Creeping Jenny is one that comes to mind.

Dawn