This data usage will be taken from your data allowance when the message is received. Once the message is received, it can be listened to without any further data connection & without incurring further cost.
As a matter of fact, some reports that have explored the decline of voicemail say the service is really only used by two types of people anymore: older parents and business people. But that still doesn’t lessen the annoyance of the receiver when they have to listen to the voicemail from mom and pop or the used car sales guy.

iPhone recorder apps only work because they utilize 3-way conference calls, either incoming or outgoing. The third "caller" is a recording line, provided by a service from the app's developer. Obviously, 3-way calling is a must-have feature of your iPhone for this to work, so be sure your carrier supports it. In the US, the big three all do, but some smaller carriers do not—at least not in a way these apps support.
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?