Yes, plants (legumes) do have leghemoglobin. It is actually about ten
times better at moppping up oxygen than ours. The enzyme responsible
for nitrogen fixation in the Rhizobia bacteria in the root nodules is
very sensitive to oxygen and has a half-life of about 30 minutes in
air. Most people reckon that leghaemoglobin is only partly responsible
for keeping oxygen away from nitrogenase, and that the architecture of
the nodules is more important.
Best Wishes,
Martin Hodson