My former neurologist (he moved to PA) was researching (in me and others) a condition he named gastrointestinal cephalgia; he felt that there was a definite connection between the acid; the vagus nerve involvement and migraines.
After the healing part of the Nissen, I felt wonderful; the headaches seemed to be a thing of the past; then, for the first time in 25 years+ I got the flu. Trying to vomit with a wrap is beyond belief; and since that happened, not only did my headaches come back, but I developed esophageal spasms. The spasms are fairly violent and have damaged the wrap; not enough to treat, but enough to give me heartburn again.,
So, the short answer to a long story is..yes, heartburn can be a mitigating factor in migraine.