Simple test:

# ModuleA.pm

use ModuleB;

BEGIN {
    print "ModuleA::BEGIN\n";
}

1;

# ModuleB.pm
BEGIN {
    print "ModuleB::BEGIN\n";
}

1;

# main.pl

use ModuleA;
use ModuleB;

BEGIN {
    print "main::BEGIN\n";
}
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Create those 3 files, then run main.pl.

$ perl main.pl 
ModuleB::BEGIN
ModuleA::BEGIN
main::BEGIN
[download]

It looks like perl does "the right thing".
--
Mike