No you can’t. I just called and asked for it to be turned off completely and was told it is impossible. It’s aggravating to get conflicting information. Obviously either the CS Team member who wrote the previous post, or the employee I just spoke to on the phone, doesn’t know what they’re talking about.
14. Hi, you’ve reached [business name]. We can’t take your call at the moment, but if you leave your name and number, the next available team member will return your call as soon as possible.

Your voicemail greeting can make a positive or negative impression on people. By considering your target audience and tone, you should be able to keep it positive. Length: Don’t make people wait minutes to leave a message. Apologies: If people expect your to be available, apologize for missing their call. Set expectations: Let people know when they may receive a callback, but be realistic. Accuracy: If you change your voicemail for things like holidays, be sure to update it when needed. How do You Set Up a Business Voicemail?
If your carrier supports the iPhone voicemail feature, you can retrieve and listen to your voicemail right from within the “Phone” app and call your contacts back by simply tapping their messages. That type of functionality is pretty neat and useful, because it saves you actual time. If not supported by your carrier, you will not be able to see the visual overview of your voicemail inbox and use any of the related features. Tapping the “Voicemail” tab in your “Phone” app will simply call the number associated with your voicemail box. So let’s get going with creating our custom voicemail greeting on iPhone! How to record your own Voicemail on iPhone Phone → Voicemail → Greeting → Custom → Record → Save