Is there a genetic component to leukemia?

There can be. But not in the sense that it is inherited within family members. An example is those individuals affected by down's syndrome have an abnormal chromosome and acute leukemia has a higher incidence in this population.
Complicated. I agree with above. Also, leukemia cells often have abnormal genetics (this is not inherited, but represent genetic changes that have occurred to the leukemia cells themselves). The abnormal genetics may provide a way that the leukemia has developed a way to grow unchecked by the body. The specific genetics of childhood leuekemias help determine treatment.