I have recently converted a GreaseMonkey script of mine into a WebExtension, just to get a first impression of the process. Now I have a reached a point where it would be nice to do some clean-up or simply undo all my changes when said extension is disabled/uninstalled.
From what I've seen on Mozilla's pages, runtime.onSuspend should do the trick. Unfortunately, it looks like that's not yet implemented (I'm on the regular Firefox release channel).
In other words, what I want to do is run code as a result of the user removing/disabling my extension so that I can clean-up listeners and such and generally restore the tabs to their status quo, i. e., undo all the changes the extension made.
Your initial wording was somewhat unclear as to exactly what you desire. Thus, this answer also contains information on one way you could receive a notification of the uninstall, under some conditions.
Run code in your WebExtension add-on prior to uninstall/disable:
No, even if it was supported, the runtime.onSuspend event would not do what you want. It's used to signal Event Pages that they are about to be unloaded. Even Pages are unloaded routinely when the handling of the events they are listening for has completed. It is not an indication that the extension is being uninstalled.
"Determine" that your "WebExtension was disabled/uninstalled":
If your question is really what you state in the last line of your question: "... is there a way to determine whether a WebExtension was disabled/uninstalled?" Then, it looks like you could use runtime.setUninstallURL(), which was implemented as of Firefox 47. This will allow you to set a URL to visit when the add-on is uninstalled. This could be used on your server to note that the add-on was uninstalled. It does not inform your WebExtension that it was uninstalled, nor permit you to run code in your WebExtension when that happens.
Unfortunately, you can not use detecting, in your WebExtension, that this URL was visited as indicating your WebExtension is being uninstalled/disabled. Based on testing, this URL is visited after the WebExtension has been completely uninstalled. In addition, it is not visited upon the WebExtension being disabled, nor when uninstalled after being disabled. It is only visited when the WebExtension is uninstalled while the add-on is enabled. From the fact that this is a JavaScript call which is only run when the extension is enabled, one would expect that the page would only be opened when leaving the enabled state.
Testing was done by adding the following line to a WebExtension and seeing when the page was opened:
chrome.runtime.setUninstallURL("http://www.google.com");
Given how this actually functions (only visited if the WebExtension is enabled and directly uninstalled), using this as "a way to determine whether a WebExtension was disabled/uninstalled" will only be partially effective. As should be clear, you will not be notified by a visit to this URL if the add-on is disabled prior to being uninstalled.