Results on Panasonic EZ950 (4k oled) that I’ve been using for a while:
240pX3: Yes, if mode is tweaked to look like 1366×768 which is one of the few supported PC modes. For 960×240 (L3 generic 4:3), parameters are H.samplerate=1317, H.synclen=54, H.backporch=156, H.active= 1026, V.synclen=3, V.backporch=2, V.active=256.
NES/SNES 240p: Works only on Line3x generic modes (also see above note), and TVP HPLL2x option must be enabled.
Line count tolerance seems to be higher than on the Panasonic plasmas that I’ve used before, so Neo-Geo / PAL PSX should not cause issues although I’ve not tried myself. 240p<->480i switching is very fast. The only major downside with the TV is that in game mode aspect is forced to 16:9, so there’s no good way to display non-widescreen 480i/480p games without stretching.