Yes, transportation of used nuclear fuel is safe because the shipping packages are very robust and because the shipments are highly regulated by the NRC and the Department of Transportation.
According to a U.S. Department of Energy (DOE) report prepared by the Oak Ridge National Laboratory and Argonne National Laboratory, more than 25,000 shipments of used nuclear fuel have been made worldwide to date, shipping more than 87,000 metric tons of fuel. Review of the data sources shows that all of these shipments were undertaken without any injury or loss of life.
In the U.S., except for a limited amount of transport, the majority of used nuclear fuel remains at the reactor sites. Nevertheless, more than 1,300 used fuel shipments have been completed safely over the past 35 years in the U.S., according to the NRC, with most shipments performed by rail. Thanks to the robust transportation cask designs and stringent safety measures adopted by the industry, every one of these used fuel shipments has been safely completed with no release of radioactivity or environmental damage.