Wouldn't successful simply mean Britain makes peace with Germany? It is my understanding Sealion was done with the purpose of forcing Britain to make peace, not to conquer it.
So I guess it could be successful if Britain realize Germany is really going to do it, there is nationwide panic and Churchill is either overthrown or sues for peace. This might be possible if Dynamo fails horribly.
Even discounting how unlikely this is, all it does is get peace with Britain, it doesn't defeat them. Britain would remain implacably hostile to Germany. Any peace that removes Britain's ability to defend themselves will be rejected, no matter how panicked the populace got.