if you're using the built in birthday calendar that pulls from the address book, then no. you can either set up birthdays manually or you can use a script or plug-in to add an alert.
I do this 2 different ways with different calendars.
1: I use the calendar widget that comes on a Mac with the widget iCal Events sized and placed right below it. http://www.benkazez.com/icalevents.php
2: Export the Birthday calendar from iCal to the desktop then import back in to a calendar or make a new calendar to import it into. Now you can add an Alarm to the birthdays. You will have to add New Birthdays to the New Birthday calendar as they won't be updated from the address book.