My current SCCM 2012 SP1 infrastructure looks like this:

CAS -> PRI 

In the PRI site I have distribution points at remote sites.

I know I don't need a CAS since I only have one Primary site, but during initial installation there was business politics that wanted us to have more than one Site Code. Instead of getting rid of the CAS I kept it just in case. Regardless...

I have a Software Update Point installed on the CAS and the PRI site servers. Software update points are healthy and working correctly. I have an ADR that deploys Endpoint definitions successfully. My ultimate goal is that we move our OS updating from WSUS to SCCM.

My question is this...would I benefit from installing Software Update Points at the remote distribution points? 

The way I understand how software updates work is that the auto deployment rule runs, finds what applies to the rule and creates the package from WSUS. It then distributes the packages to the remote DP's. Do I gain anything by having WSUS and a SUP installed remotely? 

"would I benefit from installing Software Update Points at the remote distribution points? "

No. Clients do not use SUPs based on location. Multiple SUPs within a primary site are for high availability and cross-forest scenarios only.

Additionally, SUPs only handle and provide the update catalog/metadata, they do not in any way handle the update binaries (DPs do) so having them at remote locations provides minimal value in most cases.