In theory, bearded irises of any class could be crossed with each other and produce viable seeds. In practice, individual cultivars vary greatly in terms of fertility and compatibility with other irises. The only way to know for sure is to try (although most IB's are infertile, so working with them is likely to be frustrating, if you want to breed IBs look for those that have Iris aphylla in their parentage).
Yes, it is easily possible to breed seedlings that don't really fit any class.
Keep in mind that modern garden irises are the result of crossing many different wild species and genetic manipulation through the creation of tetraploid and amphidiploid plants. Iris genetics are complicated to say the least.
