I have a book being professionally printed which has cmyk images and black and white images (illustrations) which are saved as 20% dot gain tiffs. Would there be any problems printing this from the printers since there's two different colour profiles?
Greyscale is merely the black plate, or K in CMYK. If there is no other color information for a particular image, then only the black plate will be burned into the plate.
It's really no different than printing black type in a CMYK piece.... just the black plate.
You may actually get better image results by using a rich black rather than greyscale. But that ultimately depends on what you wish to achieve with the images.