Concerning direct RF coupling to the supply: you supply your PA from the DC supply through a decoupling network (quarter wave+decoupling caps, maybe aslo ferrite bead sometimes). This will trap any RF from coupling through to your DC suply.
Concerning Radiation? No, radiation is too small and attenuated that it will not cause a damage to a DC supply, as flatulent described above.
Concerning direct RF coupling to the supply: you supply your PA from the DC supply through a decoupling network (quarter wave+decoupling caps, maybe aslo ferrite bead sometimes). This will trap any RF from coupling through to your DC suply.
Concerning Radiation? No, radiation is too small and attenuated that it will not cause a damage to a DC supply, as flatulent described above.