I would define a rational being as someone that aimed to maximise the utility whilst trying to minimise the costs. Addiction is something that people do because, a. they enjoy doing it, and b. there may be psychological or chemical reactions occurring that increase the cost of not consuming the good/service.
Therefore I would believe addiction to be rational because people generally do it because they enjoy doing it and thus it maximises their utility. However because they are addicted to it perhaps they are doing it many times, and this may result in the marginal utility gained decreasing over time. So in the long-run addiction isn’t rational if the utility of its consumption decreases.
Also we would generally assume that there are certain costs associated with addiction. If one is addicted to nicotine and smoking the cost is that they may die younger of cancer, there are also shorter term costs such as bad teeth, the smell, the monetary cost of purchasing cigarettes, the environmental damages, the monetary costs to the NHS, coughing and perhaps other physical problems. With an addiction we would also assume the cost, if there is one, would increase the more one consumes the good.
Hence we could assume that the marginal cost of an addiction is high and the marginal utility gained is low, so therefore I believe that in the long run addiction is irrational but in the short run it is rational. This is because in the short run the utility from consumption is high and the costs are relatively low but in the long run the costs increase and the utility gained falls. The reason people may still consume a good in the long run despite the increasing costs and lower utility, may be down to psychological reasons, for example it may be second-nature for them as well as the chemical affects.