I think it'd be useful if, in the Resources, we had a downloads category for modifications to third party software to integrate with IP.Board (such as login modules for other apps to connect them to IPB)

I wouldn't be opposed to this, however are there any out there to add? I wouldn't want to create an empty category because some day it may get populated.

Well, there's already plugins for software like Kayako to plug it into IPB. It also can't hurt to showcase that your existing stuff works with IPB.