Here’s the short answer: it depends on what you eat, whether you cook from scratch, and whether you eat vegetables and a varied diet (some vegans don’t like vegetables and get stuck eating pasta, bread and rice, as do meat-eaters).
Here’s the long answer: no diet, neither meat-based nor plant-based, is healthy and complete nutritionally speaking ‘just because’. Any dietary choice can be healthy or unhealthy. What you are looking for is a balanced diet that contains all the nutritional elements in the correct proportions. So while it would be technically vegan to live on potato chips, cookies, squidgy bread and soda, that certainly wouldn’t constitute a healthy or balanced diet.