It sure can, you just have to be willing to think about it instead of copying/pasting.

{
    local $dbh->{AutoCommit} = 0;  # enable transactions, if possible
    local $dbh->{RaiseError} = 1;

    local $@;
    eval {
        foo(...)        # do lots of work here
        bar(...)        # including inserts
        baz(...)        # and updates
        $dbh->commit;   # commit the changes if we get this far
    };

    if ($@) {
        warn "Transaction aborted because $@";
        eval { $dbh->rollback };
    }
}
# Note, RaiseError and AutoCommit now revert to previous state.
[download]

...just one of a number of ways to adapt the example code.

That particular example uses Try::Tiny, the dependencies of which are all core.