It seems that this question or something similar has come up in the past.
I'm not 100% certain, but I believe the conclusion at the time was that the HR hitter was not required to run the bases, but if he chose to do so, he needed to do it legally
and was subject to appeal for missing a base.
I have two options here:
1. WWMD (What Would Mike Do?)
2. Try to find the old thread
I think I'll wait for Mike to chime in before I go searching for the old thread....