Yes! This is possible and very easily achievable. It can be done with any software using the eBUS SDK and supports this feature. The image below are from the FLIR software GEV Demo, which is available for download here.

The command for saving all the current settings to the camera is found under GEV Device Control/Camera Control. The command is SensorSetDefaults.
This command will make all the GenICam parameters persistent and the camera will remember this between startups, which can be very useful.

Currently only valid for A15, A35 and A65 cameras.