If you send a CRT an image larger than it can display, it will either display nothing, some garbage or as much of the image as it possibly can - normally cropping the top left corner.

I suppose it depends if your CRT is capable of displaying a 720p signal. If it’s not, then it won’t work.

Likewise if your converter requires the input format to match what the CRT expects (i.e. it doesn’t have scaling built in), then the converter may not work either.

You might want to purchase a scaler rather than connect your computer directly to the screens.

justification: those old screens are going to need a low resolution like 480i and modern games/apps are just not designed for that so they may not run at all, or you may find that some elements like menu items are cut out and don’t render properly.