I had the Bayer array removed from my A7 II (24MP) and can confirm both of these differences.
If you remove the color filter array (CFA, commonly Bayer) from a color sensor, more light reaches the sensor. A camera set to ISO 100 behaves as though it is recording at about ISO 200. But the meter in the camera reacts to that and reduces the exposure accordingly. The ISO settings in a camera that never had a color array would actually display the correct ISO.
On removing the CFA, the camera's JPEG will display a magenta image unless you also set it to display as B&W. But the camera will have used demosaicing to create the JPEG so you don't want to use it. Instead, shoot raw and use
Monochrome2DNG to convert the raw file to a DNG which sets a flag to tell most raw conversion programs to skip the demosaicing process. This step is critical to obtain the primary benefit, an increase in sharpness. A camera designed to capture only B&W in the first place will already have this flag set.
When I compare the results for the converted A7 II to the Z7 (45.7MP) using the same lens, the sharpness is too close to tell them apart showing that there is an increase of about 100% in area resolution, about a 40% increase in linear sharpness.
But there is a lot more to it than just these mechanical differences.
A scene with good apparent color contrast might not actually have enough tonal contrast since two adjacent colors might have similar luminance. Although you can separate the colors during the raw conversion the side effects may not be optimal. Since this adjustment is often done to darken a blue sky, traditional color filters can help if you are using a monochrome camera but they are unnecessary if the CFA is present.
By viewing the image on the camera's LCD as a B&W image you can judge the amount of tonal contrast that will come through when the color contrast is no longer involved. This can be useful even if you don't remove the CFA and just convert the color image to B&W on your computer.
I had the Bayer array removed from my A7 II (24MP)... (