Yes, but with a slight correction. In the religious sense, each god cannot or would not fulfil all the wishes. For example Saraswati can give us inspiration and the impulse to right action but for harmony and love we have Lakshmi ji. Even when they fulfil the same function they do it differently. Thus, both Shiva and Krishna can grant liberation but Shiva does it by taking the soul away from the world whereas Sri Krishna by taking us through the world.
As to the wishes in generally, it is rarely that it reaches the great gods. There are plenty of little gods in the vital domain who do that.
Affectionately,
Alok Da
