The immune cells are trivial to remove; a few minutes in a centrifuge is all that is required. Even antibodies can be separated out pretty easily (though I haven't done it myself). The problem is the quantity and quality of the product. And blood alone isn't sufficient; it doesn't contain enough glucose and other metabolites to sustain cells for long (since it's continuously circulating and levels are maintained by the body, which isn't true for a culture flask).