I think that it has a chance to increase sales but I don`t think it would be extremely beneficial.
Lets say it is for 30 days.
Here is what I would analyze before trying it. How much will it cost to implement, manage, and market? You have to have some sort of tracking system whether electronic or other. Manage it and monitor for cheating. Lay out the rules before hand which people must agree too, to participate. Then market that you are having the contest. Add up all those costs and keep them in mind.
Now for the profit side. Take your average number of buyers per month and get 1% of that number. So if your average number of buyers is 100 per month your 1% is obviously 1. This means that you are likely to have 1 person per hundred participate.
Where did I get this data? It`s called The1 Percenters. 1 percent of people do most of the work in forums, in clicking web ads, etc... It`s documented fairly well.
If that 1% will offset the cost then it is worth it. Like all rules, this always works, except when it doesn`t. If you think you can beat the numbers then I say go for it.
Arm Your Toolbox