David, to answer your question, the transmission (when new or newly rebuilt) makes almost zero noise. The same is true for a freshly rebuilt transfer case. If the whine is loud and obnoxious it is time for a rebuild, however, generally speaking the 4 speed is bullet proof and with proper lube will not leave you stranded.
It is worth noting that while a 4 speed can obviously have a whine, the first place I would look would be the transfer case. Did that get changed? The idler shaft in the TC is notorious for noise after a little wear.
If the input bearing on the tranny is bad, as ErikinSC mentioned, just replacing the bearing will abate most of the noise but a bad bearing will also have affected wear patterns on the gear cluster, i.e. will never be perfectly quiet.
Rebuild kits for the transmission are available for ~ $200 and contain only bearings and gaskets.
EDIT: I don't have a lot on the agenda today if you would like to have someone else give it a listen. @jfz80 may also be about.