Would you call the affair between Alyohin and Anna platonic or consummate? 

I would call their affair strictly a platonic one. In the story, "About Love", the love affair between Aloyhin and Anna is magnified. The story narrates their love but the love shown so far in the story is not the consummate but the platonic one. Their love was the love of a feeling not of sensuality. Unlike Pelageya, they love the idea or the soul of each other. Alyohin is fascinated toward Anna spiritually, Similarly, Anna is the mother of two children but still is seen carried away by Alyohin. They spend hours together in silence. They talk, But they never consummate their pure and sacred love. In fact, the course of their love deepens but such depth leads them to the imaginations they develop for each other. In this sense, this is not a love for attraction and sexual pleasure rather a love of spiritual bond. Anna and Alyohin are  nowhere seen involved in the physical activities. Their love is silent and deep. This is a love in which they admire each other's ideas. Alyohin goes together in the theatre, spends time with her in her house and so on but he never looks at her with sexual passion. He even doesn't confess his love by being worried about her and her family, so does Anna. To be specific, they love but the love they do doesn't end in sex. They separate finally forever and show that how ideally, how platonically and how spiritually they love.