No--x-rays will not make anything radioactive. Gamma rays can only do so when they're in the 2GeV range or higher (indirectly, through pair production.)
It's particles that make things radioactive, mostly neutrons as they aren't repelled by the nucleus and thus have a much easier time getting in. And while it would be hard to construct a shield out of it helium is effectively immune to becoming radioactive under neutron bombardment. And while lead isn't immune the reaction sequence produces nothing that won't be contained by the lead and it self-regenerates, enough bombardment returns it to where it started.
It's particles that make things radioactive, mostly neutrons as they aren't repelled by the nucleus and thus have a much easier time getting in. And while it would be hard to construct a shield out of it helium is effectively immune to becoming radioactive under neutron bombardment. And while lead isn't immune the reaction sequence produces nothing that won't be contained by the lead and it self-regenerates, enough bombardment returns it to where it started.