Is it generally no issue to drink pure olive oil for the atkins diet?

Olive oil: If you mean grabbing a cup of olive oil and drinking, the answer is no. That is not a balanced healthy diet, and neither is atkins. Eating lean protein is fine, but should be balanced with vegetables and fruit. Eating a bunch of fat (fatty meat, oil, etc) is not healthy. Atkins may make you lose weight, but it does so at the expense of causing other problems.