No, it wouldn't. Labor had 72 of 150 lower house seats, and less than 50% of the senate.
Let's look at the numbers. Labor and the Coalition each won 72 seats in the 150-seat House of Representatives, four short of the requirement for majority government. Four crossbench MPs, Greens Adam Bandt and independents Andrew Wilkie, Rob Oakeshott and Tony Windsor allowed Labor to form government.
The bill required 76 votes in the House of Representatives to be supported.
Adam Bandt voted yes.
Andrew Wilkie voted yes.
Robert Oakeshott voted yes.
Tony Windsor voted no.
"On Wednesday, just 42 MPs in the Lower House supported a private members bill put forward by Labor backbencher Stephen Jones while 98 MPs voted against."
http://www.abc.net.au/news/2012-09-20/senate-votes-down-same-sex-marriage-bill/4272366
This maths is probaby wrong but 42 - 3 = 39 Labor MPs that supported marriage equality leaving 33 not supporting. It's hard to argue that Labor didn't defeat this bill. If 72 Labor MPs had supported the bill and it had failed due to a lack of support from the crossbench MPs, you could say the crossbench MPs defeated the bill.
https://www.getup.org.au/campaigns/marriage-equality/roll-call/how-your-representatives-voted
Out of 76 Senators, there were 31 Labor, 2 Democratic Labor, 9 Greens, 1 Independent, 28 Liberal and 5 Nationals. The bill would have required 39 'yes' votes to be supported. Labor and the Greens voting together controlled 40 votes. This would have been enough to get the bill over the line.
9 Greens and 1 Independent support the bill, already giving 10 votes. In the upper house, 29 out of 31 Labor Senators would have needed to support the bill for it to pass. However, only 16 Labor Senators supported it.
The bill was effectively defeated by Labor in the Upper House.
You could argue that in the lower house, the bill was defeated due to a lack of support by Labor and a crossbencher. However, in the upper house, the bill was defeated due to a lack of support by Labor.
26 in favour and 41 against