I've played around with the OSSC, but I'll cop to not owning one. Your best bet on most 240p signals is the line tripler (Lx3) because it basically creates a signal that is 720p. Granted it's a modified 720p (I think 1440x720 but cropped, but it may be 1280x720) so compatibility with certain TVs will vary. Apparently 1080p Sonys and Samsungs have shown great results whereas it varies widely with 4K TVs. Keep in mind that SNES can be a problem since it actually outputs 256x240 so Lx3 actually gives you 1024x720, which is even more off spec for 720p. I've also heard TG-16/PC-Engine has similar problems (it's also 256x240) but at the time I played with an OSSC (late last year) I didn't have an RGB modded console.
You may also have to fiddle with "normal" viewing mode (ie: overscan cropped/zoomed) and "full pixel" or "screen fit" (ie: no overscan crop/zoom) on your TV as well. This is a setting necessary with most scalers and PC sources on HDTVs, but not an issue with most PC monitors. You can also add scanlines, which many like, and the OSSC does a rock solid job at Lx3. There is also a Line 4x and Line 5x mode for higher resolutions that have been added in the recent firmware, but I can't speak to how well those will work since the resolutions are even more modified and compatibility varies.
If you want to get a feel for compatibility, the OSSC forums have some helpful folks that have created compatibility charts (keep in mind you may have to convert model numbers for EU or NA) but it's a good starting point:
https://www.videogameperfection.com/forums/topic/tv-compatibility/ You could also, obviously, just play with the settings and see what works and what doesn't. You shouldn't worry about harming your display, it'll either show the picture or give you a "no signal" or "incompatible signal" message. Keep in mind with most sources there will be horizontal and even vertical bars/black areas on your screen, so it's a good idea to give your TV a rest every 2 hours or so with some full screen content. Usually I just switch to a TV show that's full screen and play about 10 minutes to get the pixels moving. I also then take at least 30 mins with the screen off, but honestly it probably has no affect on the lifetime of the display and it has no effect on prevention of burn-in or dead pixels.