No, they did not. Electrolysis was around before WebExtensions. Sure, Electrolysis wasn't backwards compatible and a lot of existing extensions had to rewrite part of their code to be compatible, and abandoned extensions were broken forever - or would have been once mozilla removed compat shims (unless somebody picked up the slack, which people quite often did). This was still a lot better than breaking every extension and forcing a new extremely restricted WebExtensions API that was a clone of the Chrome APIs but came with their own bugs and a lot of "TODO: implement actual API".
Quantum is just a PR term. The impact of Quantum-related changes to extensions was tiny if present at all (if the extension already survived Electrolysis).
The only reason that old non-webext extensions do not work anymore in Firefox at all is that they helpfully removed the actually code that would run the extension (but not really last I checked, it's still around to support mozilla-owned sideloaded/builtin extensions such as pocket).
comm-central (Thunderbird, Seamonkey) even implemented their own implementation of what was removed to get (restartless) old-style extensions working again, falsifying the claim that forcing a WebExtensions-only change was a requirement to get e10s/Quantum going.
Underneath it all, to this day most of Firefox is still javascript + XUL/HTML on the frontend with bridges (XPCOM, etc) to expose the C components.
PS: e10s shipped in v53, "old" extensions were only removed in Quantum, which was v57 (but not really removed, as I noted, just disabled for everybody except mozilla's own stuff).
I ran (and sometimes still run) a personal fork of 60esr (aka >57 ;) where I added back "old" extension support by git-reverting a few hundreds of lines of code that they removed.. That thing was Quantum too, all the Quantum perf/speed improvements were still present, and yet magically still supported all the old extensions I cared about.