Yes, as long as the calls go through framework code paths that demand
FileIOPermission.

Not if there's already a "downstream" demand.

There's really no need to duplicate permission demands in this way.  If you
want to communicate your assembly's minimum required permission set,
consider using assembly-level RequestMinimum permission attributes instead.

In general, one only makes CAS permission demands in code that makes
assertions and/or defines or extends a resource that requires protection.
In practice, most of the latter also make assertions (usually for permission
to call into unmanaged code), so most projects aren't likely to need
permission demands that aren't coupled with assertions.  Then again, since
most projects shouldn't need assertions, they probably shouldn't need any
explicit demands for CAS permissions either... ;)