Anyone ever grow watermelons?

Our neighbor gave my sons a few watermelon and cantaloupe seeds (they like to help him with his tomato plants and blueberry bushes). They were eating the melons, and he gave them the seeds to "plant." I thought I'd humor them, so we planted the seeds in small pots with some miracle grow potting soil. I can't believe it, but they both sprouted and we have seedlings now! My boys are ecstatic and want to grow vines/fruit. The problem is, we live in Georgia and have VERY poor soil--it's 100% red clay and the only thing that'll grow in our yard is clover and chickweed, lol. Is it possible I can plant their seedlings and have them amount to actual plants with fruit that we can eat? If so, how would I go about it? I've read that they like loose soil and a lot of sunlight. If I dig up the hard clay really well and mix in a bunch of good quality potting soil, do you think they'd grow? Please help! My kids are ecstatic about this and if the plants died they'd be very upset.