In practice, yes. Often, leave will take the form of FMLA, at least at the outset. The ADA typically becomes an issue once you have exhausted FMLA leave, though there are exceptions. Consider an employee who has been employed for only 3 months. They are not eligible for FMLA because they have not worked for the employer for 12 months, which is a requirement for FMLA eligibility. If an employee needs leave from the job in the first year of employment because of a disability, the ADA would provide greater protection because the employer may be obligated to provide the employee a reasonable accommodation—that is, a leave of absence—to help the employee perform the duties of the job, absent some undue hardship to the employer.
