No, it’s something we will keep hearing about and nobody will get to try it. OpenAI is anything but open. Looks like great tech, but it’s irrelevant if it’s totally inaccessible.
Not specifically DALL-E, but you can play with MindsEye beta, which is quite easy to run, considering the complexity of all this stuff: https://multimodal.art/mindseye
It doesn't get close to the quality of the art pictures produced using DALL-E, but it's nice to play with.