I would not make the same change. Why bother wrapping an "X or die" inside an eval, then check whether X is false afterwards?

if ($dbh = DBI->do('dbi:mysql: xxxxx','root','')) {
    print "Table exists\n"
} 
else {
    print "Table does not exists";
}
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Of course, all it checks is whether one can connect - not whether a database exists (title question) or whether a table exists (message printed).