It is certainly possible - as shown on the DIAC website. Please see the link below:
It is preferable to get State sponsorship if possible. There is no doubt about that.
However, if there is any doubt about whether the applicant can get SS plus make a visa application prior to 30/06/2012 but there is a possibility of a Family sponsor instead, it makes sense to get the Family sponsor lined up and ready to roll just in case State sponsorship cannot be secured in time.
The Australian Government's Financial Year ends on 30th June each year. From 1st July 2012, they intend to introduce an Expression of Interest system with GSM visas. To avoid having to go down the EOI route, we will see a flurry of last minute sc 176 applications made, where the applicant uses a Family sponsor because there is no time left to do anything else. I certainly wouldn't advise anybody just to give up and resign themselves to the new EOI process if a Family sponsor could enable submission of a valid application for an sc 176 prior to the end of the current Financial Year.
At the moment, the Government is not sanguine about GSM applicants who use Family sponsors. DIAC did some research about the whole thing 2-3 years ago and concluded that:-
1. People who have used a Family sponsor are less likely to ditch Australia and return home. Part of the intention of the Immigration policy is to boost the economy by encouraging migration, so someone who is able to settle happily and successfully is a "successful migrant" from the Govt point of view. That is, s/he will stay in Oz and pay taxes, any children will become the next generation of tax payers etc.
2. BUT - the research also showed that new migrants with Family sponsors tend to make a bee line for the place where the Sponsor is living rather than heading for the place that actually needs the new migrant's skills. Consequently, the new migrant often doesn't continue to work in the occupation that secured the GSM visa in the first place - instead, the new migrant just grabs whatever work is available in the area close to where s/he and the Family sponsor have all chosen to settle. This makes for "successful immigration" in one sense but it doesn't help to solve Australia's skills shortage. Also it causes the local Aussies to grumble that jobs that they could have done are being pinched by immigrant workers and so on.
The research therefore produced conflicting results and the Government decided to focus on the skills shortage and hope for the best with the rest, as it were.
There is a paper about all this, kicking around somewhere and it can be found via the DIAC website somewhere. It is also discussed briefly in one of DIAC's Annual Reports.
This research is the main reason for the recent emphasis on State sponsorship but no Immigration system is ever going to be perfect, so there will be a flurry of last minute sc 176 applicants who are relying on Family sponsors, I predict.