It's not a listed benefit. And unequivocally F passengers get priority. I don't always ask, especially when my flights are just trans-Tasman and a spa session really is better for a long-haul pax. But have done so when:
- I will only be in the lounge for a short time so have a very specific time window (eg, 10am or 10:30am) - so I think no harm in asking; or
- when I know there are no F flights for the next 4 hours from my entry to the lounge, so there'll be no F bookings and I can get the certainty of a session and plan my leisurely lounge arrival and meal accordingly.
Think I'm 100% successful in MEL thanks to the terrific attitude of the F host staff there (eg re-arranging times when my inbound aircraft have been late) - although the SST have not always been that receptive to my requests! Haven't asked much out of SYD. Think it has also been 100% but would only be a couple of times at most so not a good sample size.
F Hosts and spa staff know me - and know that the simple treatment I have is of great benefit to me - so that might help.
I have posted it here because that's the nature of this site and we should all get the benefit of others' experiences. But it's not something I want (or would like others) to abuse - as it would probably be shut down completely.