Is there a way I can take RAW color images with a Canon EOS camera while reviewing them in B&W on the LCD screen on the back of the camera? Sometimes I might want a color image but would like to use the monochrome preview to help with composition.
First, let's remind ourselves of what a raw file is. It is a set of single luminance values for each pixel on the sensor. As such there is no color information to a raw file. Color is derived by comparing adjoining pixels that are filtered for one of three colors with a Bayer mask. But just like putting a red filter in front of the lens when shooting black and white film didn't result in a monochromatic red photo, the Bayer mask in front of monochromatic pixels doesn't create color either. What it does is change the tonal value (how bright or how dark the luminance value of a particular color is recorded) of various colors by differing amounts. When the tonal values (gray intensities) of adjoining pixels filtered for the three different colors used in the Bayer mask are compared then colors may be interpolated from that information. This is the process we refer to as demosaicing. How much bias is given to red, green, and blue in the demosaicing process is what sets white/color balance. The gamma correction and any additional shaping of the light response curves is what sets contrast.
The image you see on the back of the LCD screen of your camera is not the raw data. It is a preview image generated by the camera by applying the in camera settings to the raw data that results in the jpeg preview image you view on the LCD. This preview image is appended to the raw file along with the data from the sensor and the EXIF information that contains the in-camera settings at the time the photo was shot.
Canon EOS cameras since mid-2005 incorporate Canon's "Picture Style" selection of various ways of processing a scene to produce a photo with certain general characteristics. Which Picture Style is selected does not affect the luminance values from each pixel in the raw data at all. Which picture style is selected does affect the way the raw data is interpreted to produce the preview image you see on the rear LCD.
You can select the Monochrome Picture Style to see a B&W preview image on an EOS camera's LCD. The raw data saved to the memory card will still include the necessary information to process the images in color later with a raw editing application. WARNING - Be sure you are saving the raw data. If you only save the pictures as jpeg images all color information will be discarded!
If you are saving your pictures in raw format when you do post processing you'll have the exact same information to work with no matter what Picture Style is selected at the time you shoot. Some applications may initially open the file using either the jpeg preview or by applying the in-camera settings active at the time the image was shot to the raw data but you are free to change those settings, without any destructive data loss, to whatever else you want in post.
Canon's Digital Photo Professional will open an image in the same Picture Style as was selected when shot. All you have to do to change it is use the drop-down menu and select another Picture Style. You can even create a "recipe" for one image and then batch apply it to all of the images before beginning to work with them. (Note: there is a setting in the preferences menu of DPP that can be set to either show original image which uses the in-camera settings or show image with recipe applied which will apply any changes you have made using DPP when viewing images with the Quick Preview module. If you shoot using the Monochrome Picture Style but want to preview the images in color then select the later and batch apply a recipe preset that includes a color Picture Style before opening them in the Quick Preview module.)
With third party raw processing applications such a Adobe's Lightroom or Camera Raw, Apple's Aperture or Photos, PhaseOne's Capture One Pro, DxO Lab's OpticsPro, etc. getting images to disply according to the in camera settings can be a bit trickier. Adobe products, for instance, totally ignore the maker notes section of a raw file's EXIF data where Canon stores information about the Picture Style selected at the time the photo was taken. Just how convoluted of a workaround is needed to accomplish such is outlined in the accepted answer to How to automatically apply a Lightroom Preset based on appropriate (Canon) Picture Style on import? In the present case of only wanting to see the monochrome previews during the shooting session, just selecting a different default profile with which to open the images will allow you to develop those raw files from whatever other starting point you so desire.
If you want to retain colour but see in black and white on the camera, just shoot in raw but set the picture style to monochrome. Note that the monochrome picture style also lets you see the effect of fitting coloured filters to the lens to alter contrast (red, green, yellow or orange). It's applied when the camera makes the JPEG file but it's also displayed on the screen in Live View. This means you can set your camera to monochrome picture style, raw quality and see what an image is going to look like in monochrome before you take it by switching on Live View and just pointing at different scenes.