Will algae grow in a saltwater pool?

Yes and yes. The basic chemistry is identical. A saltwater pool is a chlorine pool. All the SWG does is generate the FC for you everyday from the salt instead of you having to add it. If the FC gets too low, algae can start to grow.

Also realize that the SWG tend to make the pH rise faster, so more acid may be required.

In Pool School you can find discussions about the recommended levels for all the parameters.
 
As Jason mentioned a salt water pool is a chlorine pool, the salt level is only around 10% of the salt level you find in seawater. Common salt is made up of Sodium and Chlroine, the SWG passes an electric current between two metal plates through the salt water, this current breaks up the salt into its components Sodium and Chlorine, the Chlorine then goes on to work as a sanitizer just the same as if you had poured it into the pool in the form of Liquid Chlorine / Bleach.
 
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