It seems like this is the sort of situation where querying some printing companies directly for price quotes would be more useful than using their online rate calculators, since it's sort of a special case.
Because the answer is ... it probably depends on what their equipment is set up to handle! It might be cheaper, or it might not be.
(Caveat: I worked in newspaper prepress for 15 years, so what I know about it is mostly geared towards one kind of printing. I haven't worked with offset presses for printing books or with POD equipment at all.)
So, what I do know is that there are two main ways your book can be printed: either in a large press run on an offset printing press, or in small batches on a print-on-depend (POD) digital printer. I'm guessing most of the online rate quotes you've been looking at are for POD, because with most offset printers you have to contact the company directly for a quote (because there are so many variables that affect pricing). If you're getting quotes for books in relatively small quantities -- 25, 50, 200 -- you're probably getting quotes for POD. Offset printing doesn't really become economical until you're dealing in thousands of copies.
For offset printing, the press setup is more complicated and expensive for color, but most presses have a lot of flexibility in where they put color, and which colors they use -- and it
is (usually) less complicated and cheaper to have color on some pages rather than all pages. (Which is why so many newspapers don't have color on every page, because cost is terribly important in a mass-produced, disposable product like that.) So for an offset press, the answer is, probably, that it'd be more expensive than black and white all the way through, but less expensive than color on every page (you would, however, be limited in exactly WHICH pages can have color on them). However, it depends on what their press can be configured to handle. So you would need to ask them.
POD, on the other hand ... now here I haven't worked with the equipment, but my general understanding is that the POD relies on all-in-one machines that do all the collating/bundling/binding of the book as well as printing it. (I may be wrong about this; someone correct me?) They're basically big laser printers with binding capabilities. Color books are printed on a color POD machine; black-and-white ones on a black-and-white machine, which, like getting black-and-white copies made, is much cheaper. Whereas an offset press can be configured for a mix of color and black-and-white, POD books pretty much have to be printed on either the color machine or the black-and-white machine, or else you'd have a lot of hand labor inserting pages from different printers into the same book. You certainly
can print black and white on a color laser printer, but they'd probably still charge for color because it's using the color machine.
... but I really don't
know -- it's entirely possible that some POD places regularly handle a mix of color and b&w in the same book, and have a workflow set up to deal with it. And maybe some (most?) places use the same machines for black and white
or color, in which case mixing color with black-and-white pages would be a snap!
So yeah, in either case, I'd say different printers are probably going to have different capabilities, and contacting them directly is your best bet! If the first one says "no, it'd be the same price as full color" go ahead and try some more, because they might be quite different depending on what their equipment can do.
Which was a long and wordy way of giving you a simple answer, I guess.