Yes, you can send invoices to your international customers because Abillio provides you with a VAT number.
However, if your client pays in a currency other than euros, the received amount may differ depending on the currency exchange rate on the receipt day, as international transfers may take more than one day. In this case, your invoice amount will be adjusted post-factum to match the amount converted to euros.
When adding a customer, it is important to remember to enter his tax identity number (TIN) and VAT ID number. Invoices to EU businesses with a valid VAT ID and to businesses outside the EU have a 0% VAT rate. Invoices to individuals and to EU businesses without a VAT ID include VAT. See VAT rules by country for details.