The answer to the question, in brief, is “on average, no”. => vast majority of wind farms generate more CO2 than they save! Please read on.
The very intermittency of wind means intermittent operation of the gas back-up, which means that you burn more gas, and emit more CO2, per MWh, than you would if you ran the plant properly.
Duncan Seddon's paper (here) explains this. He looks at a large number of (on-shore) wind farms across Australia, and presents figures for output and efficiency. He finds that the relative output (actual annual output as a percentage of rated capacity) varies from 22 to 42%, with an average of 33%. He also finds that where the relative output is less than 32% (that is, give or take a percentage point, about the average) there are no net savings of emissions.
Only 13 English wind farms (source here) have a rolling load factor of >32%, only 7 are >33%. These 13 will be making small CO2 savings, the rest of them actually generate more CO2 than they save, this is worse than futile. It gets worse, as the turbines age, they become less efficient, so in a few years time most or all of these load factors will fall below the 32% threshold.
This is a strong argument for removing all wind farm subsidies now."