You can't be sure about the structure of the render array inside of content, so this is possible not the best method.
This may be a better solution:
{% if content.field_example|render|striptags|trim %} <p>field is not empty</p> {% endif %}
This checks if rendering the field generates any output.
But this depends, how you have configured the field format and what you try to do. For example, you could have configured to display a label if the field is empty. Then you have to adjust this. If you don't depend on the rendered output and only want to check, if the field has a value in the database, use the node object. See Berdir's answer.