The overall consensus leans greatly towards “no.”
It’s important to note that neither of these propositions has been proventhey are vague theories at most.
For one thing, the large majority of people who have a PFO don’t have migraines.

Illustration by Cindy Chung, Verywell
Not only that, PFO closure is not a minor procedure.
2019;29(2):261-270. doi:10.1016/j.nic.2019.01.006
Cleveland Clinic.Patent foramen ovale (PFO).
2017;6(4):539-545. doi:10.1016/j.iccl.2017.05.006.
2018;7(12).
doi:10.1161/JAHA.117.007146
Rayhill M, Burch R.PFO and migraine: is there a role for closure?
Haymarket Media, Inc. https://www.neurologyadvisor.com/topics/migraine-and-headache/patent-foramen-ovale-and-migraine-is-it-time-to-close-the-book/.