Yes, but you have to open the case and unscrew the motherboard to get access to the micro sd card. I updated my to a 16Gb (from 4Gb). You can also access the sd card via USB. just connect it to your computer and it should read it like any another sd card reader.
The Mini Power Adapter Hidden Camera actually only records in motion detection and does not have any other recording modes. For further assistance with this device please contact the Brickhouse technical support team at 1-800-654-7966. We would be glad to assist you on how to setup and record with this camera as well as answer any other questions you may have. - Brickhouse Security