Probably not.  In Tayag v. Lahey Clinic Hospital, Inc., the First Circuit Court of Appeals held that an employee who accompanied her husband on a 7-week “healing pilgrimage” in the Philippines was not protected under the Family and Medical Leave Act (FMLA)See 632 F.3d 788 (1st Cir. 2011).  The court reasoned that the healing pilgrimage did not qualify as medical care under the FMLA’s definitions of “health care provider” or “serious health condition.”
The only possible circumstance in which the court suggested that a healing pilgrimage might qualify for FMLA protection was in the case of religions that reject ordinary medical care—like Christian Science practitioners.  In that circumstance, the court explained that the employer would not need to provide duplicate FMLA leave for both ordinary medical care and spiritual care.
In Tayag, the employee’s husband did not reject ordinary medical care for religious reasons, so the religious exception did not apply.  The employee’s husband’s cardiologist also did not certify that the requested leave was medically necessary.  Therefore, the court held that the healing pilgrimage was not protected under the FMLA.