Hi @webmasternyc01!
Thank you for reaching out.
Yes, if you have the New Order email notification enabled, every time a customer makes an order, it will receive an email notification about it.
You can confirm if you have enabled this option in WooCommerce → Settings → Emails → New Order.
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Image URL: https://i.ibb.co/4KZpSg6/kafjnaf.png
More about email notifications here: https://woocommerce.com/document/configuring-woocommerce-settings/#email-notifications
I hope this helps!
Not working for some reason.
In this case, you want to check if the emails are being generated and sent correctly. You can do this by installing a plugin like WP Mail Logging and placing a test order.
More about this here: https://woocommerce.com/document/email-faq/#section-4
If they are being generated but not received, you could try a dedicated SMTP provider as documented here: https://docs.woocommerce.com/document/email-faq/#section-5.
Also, here is a helpful guide that deals with this issue too:
https://www.mailpoet.com/blog/woocommerce-email-not-sending/
Let us know how it goes for you!