2 Nephi 9:20 clearly states that "he knoweth all things, and there is not anything save he knows it." So yes LDS members do believe that God is omniscient. If it were not so then having faith in him would be very difficult. Ask yourself if you could have Faith in a being who was anything but omniscient? For me it brings comfort and great confidence to know that everything I bring to him in Prayer is met by the all-knowing being who loves and cares for us deeply as individuals. And because he is all knowing he can pursue "His work of bringing to pass our immortality and eternal life." (Elder Neal A. Maxwell)
