Is there a benefit/drawback to adding LIMIT 0,1 when performing SELECT on unique key field?
If MyKey is NOT NULL (see Jannes answer) and defined as a UNIQUE index in the table DDL, the only benefit of adding LIMIT 0,1 is potential clarity to viewers of the query that this is only going to return a single result. Without them having to look at the DDL to know that it is unique. However, other Database designers will be looking at the DDL anyway.

If there is any overhead of adding LIMIT 0,1 it would be very, very minuscule. 

Either way, adding it would be up to you. Do you need the clarity (how often do users view your queries)?