No, seamless gutters do not cause ice dams. Significant amounts of money have been spent trying to solve the ice dam problem. Ice dams occur when snow buildup melts during the day and refreezes when temperatures drop overnight. Snow melt on the roof is assisted by heat-loss through the attic. The water from the snow melts then refreezes when it reaches the cold surface over the soffit, where it begins to form a ridge of ice. After several days of this melting-freezing cycle, the ridge of ice can become significant enough to retain water on the roof behind it. Ice dams are typically the result of inadequate insulation and/or ventilation. Properly installed insulation will reduce the heat-loss into attic space from living-space, however, ventilation is the most often overlooked factor. Keeping the attic space well ventilated will maintain a cool dry underside of the roof. This will discourage the melting of the snow on the roof from any heat-loss. A properly insulated and ventilated attic will not only prevent ice-damming, it will save money in heating and cooling costs.
There are other instances when areas of roofs are shaded and other areas are exposed by the sun. The snow melts when exposed by the sun. The snow melts when exposed by the sun and water runs down the roof to the areas that are shaded and freezes. As stated before, the ridge of ice can become significant enough to retain water on the roof behind it and cause leaking into your home.