I think that this is possible. Because you have to remove the existing "lens" on the Go Pro to put on this shutter and the shutter doesn't actually look any bigger than the original "lens". But the case doesn't really have much room for manoeuvre.

The protective cover is quite precise and actually fits everywhere on the GoPro... So I don't think it's possible... but I don't really know and recommend you to listen elsewhere or wait for further answers.