The short answer is no. Dracaena is toxic to both cats and dogs. Or rather saponin, a chemical compound that is found in the plant, is toxic to them. A dog eating dracaena leaves can result in vomiting (sometimes with and sometimes without blood), diarrhea, weakness, drooling, loss of appetite, and depression.
Dracaena marginata, more commonly known as a dragon tree, is an attractive plant with green sword-like, red-edged leaves.