I don't know if it is just me, but I am still not 100% sure which tone you want to change. When I read:

"it would be nice to distinguish which phone to actually pick-up? There are times when users are attempting to determine which desk the sound is originating"

It sounds to me like the phone is ringing. A Page, as most people would discribe it, would involve 1 Beep as a splach (warning) tone, then the person that is making the page would start to speak. This person talking would be heard through the phones speakers. I could be reading too much into this, as people do pickup the phone even with a hands free intercom call.

So to break it down:
-Calls from an outside line ringing the phone: yes you can change the tones.
-Intercom calls from another extension that ring the phone: yes there are a couple of ring types, different then the outside caller ring tones.
-Voice intercom, where a singe "splash Tone" is heard, then the caller talks over the phone: No. That one beep is not a ring tone
-Paging, where a caller is making an annoucement to many phones, or overhead speakers, at the same time: No, that splash tone is not customizable, same as the voice intercom.