Yes. However, this option is not available with the built in Birthday Club feature. To create a Birthday Club program that sends contacts messages on the 1st of the month of their birth, target lists and trigger messages will be required.
This type of set-up requires 12 target lists, one for each month of the year, and 12 trigger messages to send to the appropriate list on the 1st of every month.
Example: December Birthdate Target List, where Birthday static "Month" field is equal to 12.

Example: December Birthdate Trigger Message, sent MONTHLY on the 1st day of the selected month, to the December Birthdays target list.
