No, the current Si534x evaluation boards (EVBs) such as the Si5345-EVB do not directly support I2C. Instead, the MCU on the board communicates with the DUT via SPI which is faster than I2C.
It is possible to modify the EVB to allow an off-board I2C master to communicate with the DUT. (However, then the EVB's MCU will not be able to communicate with the DUT by SPI until the modifications are undone.)
Here are the general modification instructions, allowing control by an off-board I2C master, using the Si5345-EVB as an example for the 64-pin Si534x-EVBs:
1. Remove R32 which is the 0 Ohm resistor connecting the MCU to the signal path driving the DUT's I2C_SEL pin. (R32 is located on the back side of the EVB underneath JP4.)
2. Remove the jumper at JP4.
3. There are no I2C bus pull-up resistors on the EVB. Therefore the off-board I2C master will need to supply these to support the I2C bus.
Steps 1 and 2 above allow the signal I2C_SEL input to the DUT to be pulled HIGH to select I2C. Now the jumpers can be removed at J36, isolating the MCU from the DUT's serial port pins, and allowing off-board control of the DUT using GND, SCLK, and SDA jumper wires such as from a ClockBuilder Pro Field Programmer.