Does adding 'LIMIT 1' to MySQL queries make them faster when you know there will only be 1 result?
Depending on the query, adding a limit clause can have a huge effect on performance. If you want only one row (or know for a fact that only one row can satisfy the query), and are not sure about how the internal optimizer will execute it (for example, WHERE clause not hitting an index and so forth), then you should definitely add a LIMIT clause.
As for optimized queries (using indexes on small tables) it probably won't matter much in performance, but again - if you are only interested in one row than add a LIMIT clause regardless.
Limit can affect the performance of the query (see comments and the link below) and it also reduces the result set that is output by MySQL. For a query in which you expect a single result there is benefits.
Moreover, limiting the result set can in fact speed the total query time as transferring large result sets use memory and potentially create temporary tables on disk. I mention this as I recently saw a application that did not use limit kill a server due to huge result sets and with limit in place the resource utilization dropped tremendously.
Check this page for more specifics: MySQL Documentation: LIMIT Optimization
The answer, in short, is yes. If you limit your result to 1, then even if you are "expecting" one result, the query will be faster because your database wont look through all your records. It will simply stop once it finds a record that matches your query.