Yes. You can split the output of one aerial, so that a separate signal runs into each input of EyeTV Diversity. In that way, you could use both tuners with just one aerial, to receive two separate channels at the same time. You will need an MCX to RF coaxial adapter to attach a standard coaxial cable to the small tuner input on the side of EyeTV Diversity.
Using a small aerial to power both tuners may not be ideal. This may work best with an larger aerial, perhaps an outdoor one. Amplification might also be needed to compensate for the split signal, to ensure good reception with both tuners.
EyeTV Diversity can not power amplified antennas directly. When choosing an amplified antenna, please choose one with separate power supply.