Does LIMIT clause makes updating faster? (Any database engine)

For example:

UPDATE tab_name SET col_name=? WHERE col_name='a_unique_str' LIMIT 1;

The column col_name has no index, but we know the 'a_unique_str' is indeed unique. Does LIMIT 1 makes such a query faster?

(It's not difficult to do a simple benchmark, but I'd like to know if it works the same way in different databases, or any possible connection with database tuning.)

(Some databases like Oracle don't have LIMIT. I suppose they all have their equivalent clauses.)