Yes, as I read the docs, that should work fine (though it might be more informative to also print the $sth->errstr instead of simply doing exit 1).  As you're simply testing for truth, it does not matter whether ->err returns an integer or not (which doesn't seem to be guaranteed).

In general, when unconditionally reading/testing error variables or methods, it's good to check the docs, because in some cases, their value is invalid unless an error did in fact occur — think of $!. In this particular case though, this is not a problem, as the docs explicitly state "the DBI resets $h->err to undef before almost all DBI method calls" (the "almost all" refers to methods irrelevant here).