Under certain conditions, yes. EU policy requires that suppliers located anywhere in the world add EU VAT to a transaction if all of the following conditions are met:
The supplier offers digital goods or services
The customer resides within an EU member state
The customer does not provide a valid VAT number during a purchase
Since each EU member state determines its own VAT rates, the exact amount of VAT added to a transaction is calculated based on the customer’s country of residence within the EU.
If you’re purchasing on behalf of an EU business that’s VAT-registered, and you specify its VAT number during a purchase, then no VAT is added to the transaction.
In this case, for tax purposes, you would report the transaction as utilizing the “VAT reverse charging mechanism”. Since you haven’t actually paid any VAT for the transaction, there’s no need to claim the VAT back from the tax authorities.