Even a 120 Hz mode to simulate CRT flicker would require a buffer since the fields get output twice as fast. The OSSC would need to buffer a full field (224 to 240 lines) while it outputs the picture. As it runs through the buffer, it gradually catches up with real time.
Depending on the captured resolution, it would require buffering between 215 kiB (320 x 224 x 24 bpp) and 461 kiB (640 x 240 x 24 bpp).
120 Hz with black frame insertion might also not create the desired effect, but a more flickery picture than CRT TVs have.
The OSSC Pro might be able to do it if the HDMI Tx permits, I guess. Hopefully @marqs or someone else involved in the design could clarify this.