Yes, you can definitely send a broadcast message using the WhatsApp API. There are a few restrictions on the type of messages you can send.
- The message that you need to send must be in the format of a message template.
- Message templates need to be pre approved by Facebook
- They must be transactional in nature. Any form of promotional messaging is discouraged and will be rejected by Facebook.
After you have a pre approved WhatsApp message template, you can send the template to your list of contacts. The process of sending the message out can differ depending on the API provider, however most API providers should allow you to send the message out to all your contacts at once.