Your OZ boarding pass would be useless as the SKL dragons will only be interested in your SQ BP.
I've heard of F pax connecting to J getting the "You are invited to the F lounge" being printed on the onward BP, but I'm not sure how true that is.
Edit: The SKL F isn't much better than the J side, so you're seriously not missing much, if anything at all. The TPR is a different story, although I don't think you have the slightest chance of getting in
