Could this be used as a means to store radioactive material?
The volume or mass of material which could be stored this way would be extremely small. OTOH, there are radioactive ion beams used in experiments which might benefit from relativistic speeds in the beam line.
A literature search on
relativistic radioactive ion beams reveals several experiments like this at relativistic energies, but the time dilation effects don't appear to be the primary motivation behind them, but rather the large energies which give better statistics for low cross-section reactions. See this paper.
They are also used specifically to have high-precision tests of special relativity: See this article.
But storage of large quantities of short-lived nuclides doesn't seem realistic. The energy demands to keep them moving would be overwhelming and not cost effective. It's better to make them as you need them.