Yes it is possible, you can connect WooCommerce with MailBluster. You can take the help of MailBluster WordPress Plugin.
You can take the help of this guide as well on how to connect your MailBluster Brand with the MailBluster WordPress Plugin using the API key. A new item named MailBluster on the admin menu will appear after installing the plugin on your WordPress site.
Click on the Configure MailBluster API Key. It will redirect you to the API Key configuration page. Here you need to provide the API Key from MailBluster.
Sign in to MailBluster, go to Settings > API Keys and then click on Create new API key. Then name your API key and click on Create API key. An API key will be generated. Copy the API key from MailBluster and Paste it into the MailBluster API configuration field of your WordPress website and click the Save Changes button. Now your MailBluster Brand will be connected with the WordPress site.
Now install the WooCommerce Plugin to your WordPress site and you are done.