Question: Is it absolutely essential to have SCL and SDA pulled up for the enumeration to work properly?
Answer: Yes, pull-up resistors are required on the SCL/SDA pins even if no device is connected. Each line should be pulled up to Vcc through a 2.2K ohm resistor. The resistors are required to allow SX2 logic to detect the "No EEPROM / Invalid EEPROM" condition. If no pull-ups are installed on SCL and SDA, the SIE will hang on serial EEPROM access.
The SX2 chip contains an I2C-compatible 'boot load' controller. The boot load controller operates when SX2 comes out of reset. and looks for a serial EEPROM on the SCL and SDA lines. If no activity is found on these pins, the chip takes control of the I2C bus and attempts to address a serial EEPROM at sub-address 000 or sub-address 001. Detailed information on the SX2 I2C compatible boot load controller and startup sequence can be found in section 6.4, EEPROM Select-Jumper JP4, in the EZ-USB SX2 Development Kit Manual Getting Started document.
