Can I cite an old book in my research proposal without having read it?
You need to read the material you cite.  That does not mean you need to read an entire book if the relevant portion is in one or a few chapters, but just plopping in a citation without ever cracking the cover is reference padding and is academic misconduct.

You've been given good advice by J. Fabian Meier about also citing newer material, but you can't cite something you haven't read.