No, require does not call import(). And you reminded me I wanted to include Exporter in the @ISA array so that the parent class inherited the import() method from Exporter (which is why this module came into the answer). This is almost equivalent to use base qw(Exporter) (but not identical). See the docs of base.

Also, if the symbols were added to @EXPORT_OK, they should be explicitly mentioned as arguments of import. To keep the answer in line with the question, using @EXPORT is the easiest thing to do.