I painted our partition wall (middle wall between 2 houses, and is not exterior facing), because it already had 3 layers of paint, but I would advise against painting exterior basement wall that are not vapour proofed from the outside.

Wouldn't the vapour eventually just bubble up your paint? Try putting clear plastic over a 2foot by 2foot spot, and seal it with tape. Does moisture collect? That could be a good test because even though you don't have water issues, "water" in the form of vapour could still be coming in.

Again, not an expert, but I was told to leave stone alone in the basement if the wall is not waterproofed/vapour proofed from the exterier.