No.

The “all browsers are iOS reskin” thing is browsers must use WebKit for JavaScript and rendering, which are the two biggest parts of a browser. WebKit is a library of code distributed as part of the iOS SDK. However, Safari adds more on top of WebKit, including its plugin API. Installing plugins into iOS Safari wont affect anything just using WebKit because they aren’t using the Safari plugins code.

In theory Firefox could implement its own plugins system for iOS, but it would more limited than the normal Firefox plugin system for other devices, and also they might run into policy issues with Apple (this policy about 3rd party browsers is part of a broader policy against side loading, which has in the past prevented things like emulators and programming apps into the App Store. They have recently started loosening up on their anti-side loading policies, however).