I don't qualify for FMLA at my job because I haven't been there long enough. My HR office suggested I apply for ADA (Americans with disabilities) to ensure my job during the surgery recovery period. Anyone know if this surgery qualifies under this? I couldn't find anything and according to what I read online it looks like the ADA is for people with more permanent issues.

There is really nothing to "apply for" under the ADA. A covered employer (assuming your employer is large enough to be covered( which it sounds like it is, since they are advising you about the ADA) has to grant a reasonable accommodation for your disability. You have to tell them you are disabled and ask for the accommodation.

The ADA defines a person with a disability as a person who has a physical or mental impairment that substantially limits one or more major life activity.

If I were you, I would get a doctors note explaining your medical condition and I would show it to them and ask for an accommodation for your disability (obesity and whatever co-morbidities you have). Explain that the accommodation you want is time off to have this surgery and recover. If they say no, talk to an employment lawyer who handles disability discrimination or your state Protection and Advocacy agency.