In short: No. Source.
It really depends on how you measure the caffeine. When coffee is roasted the beans lose some water content (somewhere in the 20% range give or take a few percent). At the same time it is losing weight it is gaining size. While you should keep in mind that coffee should be selected by personal taste (or you can check out the Top 5 Coffees in the World), this leads to a situation that makes answering this question a little interesting.
Assuming all other variables are the same, if you measure by weight you actually have more caffeine in dark roast because the water loss is faster than the minimal caffeine loss during roasting. If you measure by volume you have less caffeine because the beans expand as they roast. This seems to confuse some people so let me restate the above. If you measure your coffee using a scoop you will have less caffeine per cup using dark roast coffee. If you measure your coffee by weight you will have more caffeine per cup using a dark roast. The difference one way or the other is small.
If you are buying a cup of coffee and the coffee is measured by weight (common with pre-packed coffee used in many offices and some restaurants) then dark roast will have slightly more caffeine. If you buy a cup and the restaurant measures by volume (common when coffee is fresh ground and measured on the fly) then light roast will be slightly higher in caffeine simply because you will have more coffee grounds.This is really only an issue if you are talking about two identical coffees and even then the differences are small.
It is conceivable if you are comparing coffees from two countries entirely (or sometimes coffees from the same country, grown at different elevations) that a difference in varietals between them could make the have as much effect as the roast and the preparation method will almost certainly had a larger effect than the roast level or varietal. If there is a Robusta in one of the coffees it is almost guaranteed to have more caffeine. This is mostly an academic discussion because the differences in caffeine content are relatively small.
Another thing to consider is how sensitive your stomach is to producing acid – darker roasts are less acidic than lighter roasts – and caffeine is known to increase stomach acid production. This can be benefit after a meal (helping you digest your food), but can cause discomfort at other times.