No. Alec did not believe in the Blue Lady.

The Blue Lady was a construct made up by Ben, and exclusive to Max's unit. They did not share it with anyone else, and seeing as they did not even know they had clones, the clones couldn't have known.

The Blue Lady was something that Max's group made up to make themselves feel better. Alex is a clone and was in a different group so he had no idea about any Blue Lady

I don't think Alec actually had any kind of religion. The only one he seems to believe in is himself.