How are you testing the oscillators? Patching them to your other Euro stuff? I would guess that the VCOs still work when not receiving sync, but you may be able to check that sync is working without a scope by experimenting with the oscillators. For example by putting the VCOs in vertical range and flipping the sync switch, it should switch between a plain triangle wave and one that’s hard-synced to the field rate (60 Hz for NTSC / 50 Hz for PAL). This should sound different enough to allow figuring out if your sync generator is working correctly.
In my experience if the RGB encoder is not receiving sync, displays won’t register it at all - on my display I would get a solid blue “no input” screen, same as if I just disconnected the AV input. If you get a blue screen or “no input” indication when nothing is connected, but get a black screen when connecting to your RGB encoder, your encoder may be outputting sync but not encoding signals correctly (due to a bad solder joint / whatever).
If you are getting sync generated, I would guess you can also listen to the front panel vertical sync output to get a very low tone (50-60 Hz pulse wave) and a tone from the hsync output that may be too high-frequency to hear (>15 kHz). If you’re not getting sync output from Cadet I at all, but you don’t think there are any soldering issues or incorrect components, it might be worth trying to reprogram the microcontroller (though this will require an AVR programmer). Some discussion of the settings for doing this is here.