Question: Can the use of "use" be considered same as the include file functionality?

No. require doesn't inline the file like C's #include, and loading a file without a package using require is wrong. It definitely won't work here. (use is implemented in terms of require.)

do might do the trick, but why not just use Exporter?

package MyConstants;

use strict;
use warnings;

use Exporter qw( import );
use constant qw( );

my %constants = (
    FOO => 1,
    BAR => 2,
);

our @EXPORT      = keys(%constants);
our %EXPORT_TAGS = ( all => [ keys(%constants) ] );

constant->import(\%constants);

1;
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or

package MyConstants;

use strict;
use warnings;

use Exporter qw( import );

my %constants;
BEGIN {
    %constants = (
        FOO => 1,
        BAR => 2,
    );
}

use constant \%constants;

our @EXPORT      = keys(%constants);
our %EXPORT_TAGS = ( all => [ keys(%constants) ] );

1;
[download]