If you have schematics then it is possible to insert the video signal that comes from a b/w game into a b/w TV. However, try find a B/W TV these days......and then the schematics...
I know that it is possible because when I was young (and thus poor) I had a portable B/W TV as a monitor on my Atari 600XL and some (older) friend hacked in the monochrome (=b/w) video signal into it. It looked great.
The very first games like Computer Space had actual TV's in them, and you can bet that they hacked the video signal into them (and did not produce a HF signal from the game PCB that then would be translated back by the TV, that would give a much worse picture and would cost a lot of extra money for the HF converter on the game PCB.
Remember, an (old) TV is nothing more than a monitor with a built-in receiver. Leave out the receiver part and you have a monitor. If you can find where the receiver has decoded the HF signal (the radio emissions that used to go through the air) into the video signal, you can insert the signal of a game PCB there. So you bypass the entire HF decoding section.
Using a color TV instead of a B/W one is possible but I would only suggest it as a last resource. You can feed the video signal to the RGB connections on a SCART to get a picture. However, there are two big disadvantages:
1) convergence. A color TV is never 100% correctly converged. You will see some colors appearing in corners because of (slight) misconvergence. There's nothing to do about that. A slight misconvergence was acceptable and even specified on TV's. It's acceptable because in normal color TV use it is hardly noticeable. However, when you feed a B/W signal, especially one that is so simple as those from the really early games, it will be much more visable.
2) resolution. The old b/w tubes have a much higher resolution (dot-pitch) then color tubes. This is especially clear on B/W vector games, but it's true for all B/W games. Now, with Pong that doesn't really matter much because of the extreme blockiness of the picture, but with f.i. Computer Space or let's say Sprint, where there is much more "advanced" graphics it's more noticeable.
Still......it is a very viable solution if you can't find a real B/W option !!!
The tube size can be a problem though....23" may have been a regular size for B/W tubes, it certainly isn't for color tubes....
This is especially destructive for Video Pinball. The screen has to exactly overlap/match the playfield and the LED's so a different size tube is out of the question. That's why I pray that the one in my VP is still working....