It depends: technology is one tool which may be used to make a positive impact, but in the absence of other changes, technology alone will not alleviate poverty.
One Laptop Per Child (http://laptopfoundation.org/index.shtml), a recent initiative implemented in cooperation with schools and or governments in developing countries, has captured a lot of attention. The gist of this project is to donate or provide at a low cost basic laptop computers to children in developing countries. The goal certainly an admirable one is to "stimulate local grassroots initiatives designed to enhance and sustain over time the effectiveness of laptops as learning tools for children living in lesser-developed countries." Presumably this gives children in said countries a new tool for learning as well as the opportunity to become adept in technology which they can apply later in life.
There is no denying that this does some good. Computer skills are both useful and likely to improve the career prospects of the children who get a laptop. But will the net effect be a reduction in poverty, or will it just shift the balance in favor of those children who receive computers? It is feasible that the technology can help some, but in this case it can't help those who don't receive it the end result depends partly on how that technology is distributed.
Another crucial factor is how we frame poverty. In the US, poverty is often attributed to a lack of education or job skills, a view which considers the individual firmly in charge of his or her own destiny. From this perspective, people should simply seek out training or stay in school to avoid poverty.
However, if you look at poverty as a result of environmental factors which individuals have much less control over natural disasters, war, institutionalized discrimination, living in a state that doesn't function - the picture is very different. Technology can still play a role; meteorological advances allow better prediction of tsunamis, agricultural technology can makes crops more resistant to drought or flood, but it is a much less direct role, and applying technology as a solution is more complicated than distributing laptops.
Considering poverty as an issue of inequality rather than as one of lack of education or job skills may also provide insight.
The UNDP Gini index (http://hdrstats.undp.org/indicators/147.html)assess es the level of inequality (in income or expenditure) by country. It is interesting to note that some of the countries which most of us would agree have high access to technology also have great inequality. Is inequality the same as poverty? Not necessarily, but it is worth pointing out that the overwhelming amount of technology in the United States which is fairly widely available in public schools, at least in contrast to many countries in the world does not seem to have alleviated poverty in one of the most affluent countries in the world.
Finally, what we mean by technology affect the answer to the question at hand. To many Americans, technology means iPhones, Google Earth, and all-in-one copy machines. But Wikipedia calls a strict definition of technology "elusive", and includes as examples "material objects of use to humanity, such as machines, hardware, or utensils". (http://en.wikipedia.org/wiki/Technology)
That definition would include the Hippo Roller (http://www.hipporoller.org/), an innovation which many at first glance would not be inclined to categorize as technology. The Hippo Roller which I learned about courtesy of Beyond Good Intentions (http://www.beyondgoodintentions.org/), a soon-to-be released documentary which seeks to anser the related question "What really works in international aid?" reduces the workload women and children in the developing world who travel long distances to collect water on a daily basis. Aside from alleviating a physical burden, this invention also saves time and energy which can be better put to use in, say, school for children or income-generating work for adults. Of course, if there are no schools, or tuition is too expensive, or culture encourages parents not to educate daughters, the impact of the Hippo Roller will be less drastic. But it could well make a difference because it addresses a real and specific problem in the communities where it will be used.
The Hippo Roller is also provides a colorful example of what is perhaps the most important point: no one would expect the Hippo Roller to reduce poverty in inner-city America. Perhaps similarly, we should be cautious about expecting what works in the US or what we believe works - to have magical results in widely different contexts.
Technology can play an important role in reducing poverty, but technology alone is not enough.