It's a common knowledge that White have about 55% probability of winning the game over Black, for the equal strength opponents. Having one extra move at the beginning will give maybe extra 5%, maybe less. And one more move will probably add another 5%, bringing the probability of winning (given everything else being equal) to about 63-65%.
Since most of my games are not drawn, I would definitely go for an extra move(s) at the beginning, but statistically speaking, for the equal opponents with high draw ratio, this would be not advisable, they lose a lot of half-points for the 10% more wins.
So, here it is, if the opponents have more than 20% draw ratio, this new strategy has no advantage. If the percentage of draws is smaller than 20% -- a few extra moves will definitely help.
After some deliberation...
The effect of having a few extra moves will also greatly depend on time control the games are played with. The most impact it will have on the shorter games, with less pronounced effect for 30+ minute games or longer, that tend to end up in draw more often.