I used the advice on this thread to good effect so thought I'd share my experience. I was booked on two separate tickets, premium economy on SQ from Melbourne to Singapore, and then QR connecting to Europe through Doha, in J. I checked in with SQ at the business class line using my *G card. The agent said interlining should be no problem, looked at my QR ticket and asked if I was booked in J all the way on QR. When I asked if it would make a difference if I wasn't, she said yes, indicating that separate classes might mess up QR's system. I was a bit puzzled why the class I was flying on QR would be relevant but didn't say more. It was only after I had gone through security and immigration that I realized she had upgraded my SQ segment to J as well!

So not only will SQ interline, at least at some airports, but it seems it's possible to get an upgrade out of it as well...presumably at the generous discretion of the check-in personnel.