possibly... when in NZ a year ago I asked if my membership of the National Trust (not the Scottish one) worked in NZ, and they said it did but I needed to have my card with me, which of course I'd forgotten. Take it with you, it may well work.
According to this National Trust for Scotland website page,membership covers
"Enjoy free access to over 300 properties throughout Britain (including free admission to National Trust properties in England, Wales and Northern Ireland and others worldwide)."
It doesn't say if Australia is included in the that,but we have a National Trust membership and that does.
If you email them here:~
http://www.nts.org.uk/ContactUs/
they should be able to tell you.