Yes, Black Eyed Susan is drought tolerant. But if you want a ground cover, I would recommend Tickseed. They are drought tolerant and love the sun.
Black Eyed Susans and Tickseed both require full sun.

Here is a link that might be useful: Sooner Plant Farm drought tolerant ground covering plants

I always thought black eyed susan (variety rudbeckia goldsturm) were drought tolerant, but they have not done well in dry conditions here the last three years. I think you would be much happier with the coreopsis. Early sunrise is a very good dry tolerant one that needs full sun and it's shorter and has a longer bloom time than the rudbeckia. Also they are grown from seed, so usually economically priced. Another good choice would be to do a sedum garden. They come in many varieties, different colors, heights, from creeping 2-3", up to 24" tall. That would be very interesting.

it is 116 today here in OK and I don't know when it rained last. I was out looking to see what is still alive. I don't water much, just enough to keep it alive, not flourishing.

The rudibeckia that is still alive and blooming is Becky. All the purple coneflowers burned up a month ago.

Sedum, Walker's low catmint and several varieties of Lantana are my big drought tolerant winners.

Mexican oregano is very drought and heat tolerant. Salvia greggi"perfectly pink" i , Sedum palmerii lived through last years Texas drought and heatwave. I never watered and ny soil is very porous.