You should. It is a nice way to push up your AOV.
Free shipping isn't nessecerily a bad idea. If it used properly. It is a great gimick for getting a customer to complete a purchase during crunch times, like xmas. It is also a wonderful re-activation tool.
People buy from different sites for many different reasons, almost as many reasons as you have customers. There are plenty of people who will buy from a site soley based on a free shipping promotion. Other will buy based on the quality of the information provided. No one should sneer at anyone who targets any one type of customer There are niches that can all be tapped.
The only stupid thing any ecomm merchant can do in regards to specials/promotions/gimicks is to write off a promotion before they have tested it themselves. If you provide any sort of special service, whether a free shipping promotion or a free gift or whatever, you should test that service against not offering. You may find it helps to offer it, you made find it does nothing, you may even find it hurts your sales. Test, test, test. DO NOT ASSUME, ASSUME, ASSUME.