How likely would it be for a naturopathic doctor to identify a nutritional problem?

Very likely. Check to see that they graduated from a 4 year naturopathic medical school. If so, they will be quite expert at this.
Very likely. Nd's have, in addition to similar training in areas that md's have, exposure to many holistic approaches that don't involve medication. Nutritional concepts are integrated into their curriculum and allow for an nd to give sound advice on this topic.
Unlikely. Naturopaths use uncertified laboratories which give unrelaiable results (this has been subjected to testing and is a true statement) They have enough knowledge to identify an obvious deficiency but their training, such as it is, is oriented to finding deficiencies in every patient so they can sell their potions.