I was just wondering if a bronze member has any chance for an upgrade (ecconomy -> bis)

The reason i'm asking is that my grandmother is taking anohter trip with qantas.
But unfortunately she was not a member before
so she didn't earn any points.
I signed her up now and i see that you can request an upgrade.

any chance for a bronze member flying form
BNE at 2pm to SIN

then SIN at 11pm to Frankfurt?

thanks -David