No, the app doesn’t manage VAT or any TAX-related calculation. Wholesale Pricing Discount uses the Shopify Draft Order API as shown here.
And, we send a property "taxable = true" to the Shopify API if the product is taxable.
An alternative solution here would be to adjust discounts for the products so that they include the VAT prices. This way, we can help you showcase the VAT-exclusive prices separately to your wholesale customers. But, this will only be for display purposes.
A lot of our UK merchants use this solution. You can check one of the example stores here,