If everyone participated, but did not change their overall useage, the only effect would be a short backup in the production/transport cycle. It would be a temporaty aggtravation to oil companies, to be sure, but with no effect on prices.
Much more effective would be a series of no-drive days, perhaps on weekends, or permanent reduction in useage and changes in driving habits. This would also require people to change their habits, and buy-in would be much harder to get.
There is a long, steep hill near my neighborhood with a traffic signal at the bottom, with a two-lane left hand turn up the hill off a heavily travelled street. I call it OPEC hill, because of the untold wasted gallons of gas expended there as people in the two lanes accelerate up the hill trying to get ahead of the cars in the other lane when the left-turn light turns green. With the much-cursed gas price increases, I have observed no reduction at all in this behavior. I have commented sarcastically to my family as we go up this hill, "I see that gas prices are not too high yet."
Really, the only answer to gas prices, unless you want to induce shortages and rationing, is either increase in supply or reduction in demand. I have found that I can easily increase my mileage by 8% or more just by paying more attention to my driving habits. My wife this week started car-pooling with a co-worker who lives nearby. These kinds of things widely practiced would do more to control gas prices than all of the protests and complaints combined.