No, it won't. When rust "installs" an application, it will compile it as described in the cargo.toml, then put the resulting binary file in "~/.cargo/bin" (just looked it up to be sure). The user can then either execut from that directory directly or prefix PATH with it in his ~/.profile or similar files, making it available like any other program.

A separate package manager is not remotely needed for this and thus poses an unnecessary dependency and burden on users who didn't have homebrew installed. It integrates with the systems package manager in that it takes higher priority (well, or lower, depending on wether PATH was prepended or appended) during application lookup and does nothing else. Without looking at it I'd guess that homebrew does the same.

> I know almost nothing about cargo since I don't do rust

And you don't have to. Git clone, cargo install, add line to .profile (if not already there), done.