Unfortunately, no - Central Park is closed to traffic. The simplest way to arrive is by foot. Enter the park at Fifth Avenue and 72nd Street and follow the traffic road to the right. It is a pleasant walk and should take approximately five minutes.
The Boathouse shuttle can enter the park and will bring you to the venue entrance. The shuttle will be available at fifteen minute intervals, stopping at the corner of Fifth Avenue and 72nd Street. It also stops at 80th Street where you can park at the 24-hour Metropolitan Museum parking garage. The shuttle will also be available at the end of the evening to bring guests out of the park to those same locations.
The Boathouse does not have its own parking area but there are several garages nearby. Small parking garages may be found as close as 72nd and 73rd streets off of Fifth Avenue but the venue suggests using the Metropolitan Museum’s garage at 80th Street and Fifth Avenue. It is large enough so that you will always find a space and it is open 24 hours.