The answer is "No" you don't _need_ a heated bed for PLA but it does make the base layer a little easier to lay down and also helps with print removal post print.
PLA is a very easy filament to work with and the majority of PLA printers don't come with heated beds and suggest blue tape and/or elmers glue.
You may find that if you are purchasing very cheap/poorly extruded PLA, that things don't stick as well and a heated bed can alleviate some of these issues.