it's near impossible to do that with Saints Row, as far as I can tell.
the reason those mods can be installed and tracked so easily by the NMM is because those games are designed from the ground up to support modding, to the point of having a modular file format specifically intended to aid modders.
Saints Row is not. Despite Volition being a BIG hand to the modders recently, these games were not built with modding in mind. All Saints Row mods are made by people going into the files and hacking something together themselves with the limited resources we currently have. Which in the best case (of SR2 and SR3) is buggy alpha tools Volition's tossed our way, and in SR4's case, a handful of homebrew tools which, while great and I am immensely thankful to the people who provided them, are fiddly and often will not do what you want them to.
It's possible we might see something like what you're asking for with Saints Row V (if that ever happens) but right now the best we can hope for is for Volition to throw us the SDK. Which I have on good authority will likely not happen until at least half a year from now.