Am I correct that in addition to Unity fax integration steps, the router has to be configured for T.37? So faxes are converted to TIF's on router, and then TIF's sent to Unity?
That is correct. Take a look at the configuration example below.
Also, be aware that Unity IP Fax is intended for a small number of users and is only supported in a voicemail only environment. See the following link.
Hope this helps. If so, please rate the post.