I started training in aikido about a year after I started regular Zen practice, and I find that for me the two complement each other nicely.
Some teachers, such as Chiba Sensei, encourage zazen. In fact, there is an interesting article by Chiba Sensei at aikidoonline regarding this topic.
However, I would not say that there is any necessary correlation between the two. Aikido is not a religion, but it can lend itself to the cultivation of sincerity, which is the heart of all religious practice.