A simple window manager wouldn't be dependent on a process manager. A GUI however is going to be dependent on a process manager. Kwin and Mutter don't require systemd, KDE and Gnome do. GUIs need many processes to be running and communicating with each other. Which means when things go wrong they need to resolve it. A GUI needs to provide process management. Modern GUIs in particular, where there is an expectation of dozens of processes running notifying the user require quite sophisticated process management. Arguably the thing that drove the biggest change in Gnome 3 / KDE 4 from Gnome 2 / KDE 3 was introducing a framework dependent on much more sophisticated process management because they wanted notification to work well.
So for Linux either:
a) Each GUI provides process management and most applications can't be cross GUI
b) The GUIs agree to share a process management framework and then there is a hard dependency between the GUI and this process management framework.
In the days of Gnome 1, KDE 1/2 the world looked more like (a) where neither GUI had a desire for the other GUIs apps to run well. Linux was then in the process of forking into two incompatible operating systems. The customer base however objected to this fork and since then the move has been towards (b). There is no reason in 2015 to object to process management while using a modern GUI. FVWM, Fluxbox, Sawfish etc... never claimed to provide this kind of service so of course those window manager are likely to continue to run fine on distributions that don't use systemd. As time goes on the less sophisticated Linux products are going to need to provide viable means of running large numbers of processes that have dependencies on one another and resolving dependency issues in real time. Non process managed systems are simply not going to be supported.