If you stream over the cellular data connection, yes it will use your data.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
We are happy to answer all your Verizon Wireless questions, c4. Streaming music via Apple Music (or any other application) uses data. No worries, if you have a plan that includes Apple Music, you have unlimited data and you can stream music as long as you like at no additional cost.
Does this information clarify your concerns about data usage with Apple Music (https://www.verizonwireless.com/support/apple-music-faqs/)?