Nah, the Lounge Angels at BA Singapore are often very friendly and don't think much of who is coming in. I've entered either the QF or the BA lounges shortly after the open time with a cheapo Malaysian Y boarding pass (departing from Terminal 2), and they didn't mind at all.

From what I know, SATS is only open to QF elites only if directed from the QF Lounge due to overflow and not other circumstances.