Can a fusion correct leg pain without any back pain present?

Maybe. Not enough detail to answer accurately, but let's assume the leg pain has already been diagnosed as related to an unstable/arthritic spine. Fusion might help, but i'd want to be absolutely certain there is a definite causal relationship between any spinal findings and the leg pain before submitting to surgery. Osteopathic assessment & treatment is conservative; you might want to explore this first.
Yes . This can sometimes occur in cases of spondylolisthesis or spondylolysis where there is nerve compression or irritation leading to leg pain but not accompanied by any back pain and by doing a fusion pne eliminates the source of instability leading to the nerve symptoms.