Yes, you can. StumpWM uses a keybinding system that is very much inspired by Emacs. You can bind any keypress to any action, or even another keymap in order to create multi-key commands.
You can easily define new commands by using the "defcommand" macro. Here's an example from my config file that creates a floating group (untiled windows) and starts Android Studio in it (or switches to it if it isn't already running):
(defcommand android-studio () ()
"Start Android Studio in its own group"
(select-group-or-create ("Android Studio" :float t)
(run-shell-command "~/src/android-studio/bin/studio.sh" nil)))
StumpWM isn't just about being a great tiling window manager. It's all about the configurability. Just like Emacs without any configuration is a decent editor, but can easily be challenged by other editors, it's the ability to make it behave just the way you want to that really makes it shine.
As an example, I have built a Dbus integration module for StumpWM. It's a work in progress, but useful for daily work. It's nice to be able to exactly control which notifications are displayed and how long they stay on the screen (I'm looking at you, IDEA compilation notifications).
The kind of flexibility offered by StumpWM is hard to beat, and combined with the ability to connect SLIME to it in order to have a REPL running in Emacs directly working with the running window manager makes it, in my opinion, better than any alternative.
I'd love to be able to "right-windows o f" right windows is the leader key, o would be open, and f is for firefox. "right-windows o c" to open chrome