Can a Gas Ejector handle 2-phase flow?

To a point - Yes.

Small amounts of liquid on the LP suction side of a Gas Ejector is acceptable and can be catered for in design. 'Mist' flow and 'Annular dispersed' flow regimes are acceptable.

Liquid on the motive (HP) side can be more of a problem because unless precautions are taken, the rate of erosion may increase.