Well, offers are used the world over, especially in retail, so there must be something in that. If a customer perceives they are getting something cheaper than normal, or free, then arguably this does influence the buying decision.
The thing is, when you think about it, offers are not really genuine in 99% of cases. Everything is factored. Look at DFS - they might say 'Was £1200, now £399', but what they really want is you to give them £399 for that sofa.
However, the fact that they sell millions of sofas does show these 'offers' work. It's all in the mind.