The rate of emissions just controls how much more warming and how much sooner the existing warming will occur.
This is one of the core problems with Human responses to the problem: people think they can wait until it gets 'bad enough' then stop their emissions and things will improve. But they will keep getting worse because of the lag between emissions and effects.
As for CO2 vs Methane, Methane is responsible for about 20% of all man made warming (1). So eliminating it completely would still leave 80% of warming... This is because we emit a lot, lot more CO2 than Methane.
The division is really a false one IMHO, because a lot of methane comes from coal mining and oil/gas extraction. So unless you stop using fossil fuels (the number 1 CO2 source) you cannot stop methane emissions...