Yes and no. While eucalyptus is not considered invasive, eucalyptus trees can compete with the native plants in your garden for resources. If you were to plant eucalyptus outdoors, it would be best to house this tree in a controlled environment, such as a safe, enclosed garden. However, you may opt to take your eucalyptus plants outdoors in the sun when the weather gets warmer. This plant will grow with genuine sunlight and warmth, especially in the spring and summertime. Just make sure to bring your potted eucalyptus indoors when the weather gets too chilly.