Wouldn't this also fail if $chompstr contained \E ?

No, it's magic:

use strict;
use warnings;

my $str = 'foo\E**** <- this is a syntax error';

if ("foo" !~ m/\Q$str\E/){
    print "No syntax error\n";
}
__END__
No syntax error
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If the quoting had stopped by the embedded \E, you'd get the Nested quantifiers in regex error.