Is it Safe to Plug a Regular Power Strip (with no surge protection) into a Surge Protector Strip?
End result: It makes no difference.
A "surge protector" circuit generally just shorts surge current to ground, so even daisy-chaining them (contrary to popular belief) generally has no ill effect.

More importantly, however, when daisy-chaining any form of extension cord, outlet expander, or power strip, it becomes very easy to overload the outlet, or one of the connections in/between devices, causing a breaker to trip, or creating an electrical fire!