Yes! I have had great luck with Thungbergia or Black Eyed Susan vine in a container even smaller than yours and the secret is to use good potting soil and make sure the container has drainage.  The MiracleGrow brand is one sold at most big box stores that I have had good luck using. Other tips are to not let the young plants dry out (but don't overwater) expect to water daily in the summer as the soil is so shallow it dries out quickly. Also be sure to fertilize once the new plants settle in. Either use a slow release plant food like Osmocote worked into the soil at planting time or wait a week before watering with an all purpose plant food that is mixed into  your watering can. This vine does not need a lot of fertilizer and it does love full sun. I expect your vine will be setting off fire works of flowers and scrambling up that trellis by the 4th of July.  Keep growing, Marianne Binetti