No, beverage service gratuities are included with ‘Have It All Early Booking Bonus’.
Because those beverage service gratuities are already covered, you can order included drinks on board without an extra gratuity line appearing for those covered beverage services, which is one of those quietly wonderful details that makes the math feel kinder. If something falls outside what your package covers (such as a premium-priced item above the package limit, a specialty purchase, or another not-included service), additional charges may apply.
For the most complete context, see the full Have It All Early Booking Bonus FAQ list, and the broader Holland America guidance on gratuities and service charges.