I have seen different RTF readers format the same RTF document differently and wind up with different numbers of pages.

Therefore I don't think that what you want is truly possible.

Were I in your boat, I'd investigate whether it was possible to pass the RTF through some program that put them in a format where I could see how many pages it had. The page count that you get will be dependent on the program, but should generally be close to reality.

After a quick google, it looks like you can find rtf2ps here and then grep for %%Page: might work to count pages. (If that converter doesn't work well, then google for another one, there has to be one that works...) As a bonus you can then choose to convert the ps to pdf on the fly to render in web pages. That way if anyone complains that you got the number of pages wrong, you can always point out that different viewers get different numbers of pages, but your count matches what is in your pdf.

UPDATE: I made it clearer that my untested solution might or might not work.