If a person spends all of their assets paying for Assisted Living, will that disqualify them from getting Medicaid?

As said, you are better paying some months privately for LTC and then going on Medicaid. ALs can only care for residents suffering fro Dementia for so long, eventually they need more care than an AL can give.

When Mom started running out of money I applied to Medicaid. In NJ you have 90 days to get them the info needed, spend down and find a facility. I started the process in April. Mom moved into LTC May 1st. She paid privately for May and June taking her under the 2k cap. I called the caseworker, confirmed I did what was needed and Medicaid started July 1.

I have found that in order to enter the better rated nursing homes, it is helpful to have as many months of private pay available to the applicant as possible.

Therefore, I would suggest that you not apply after your sister has completely exhausted her assets. At that point, she would be applying for a Medicaid bed. In the better facilities, Medicaid beds go first to current residents that have exhausted their money by paying privately.

As soon as she is medically eligible for a nursing home, apply with as much money available as possible to increase her chances of being placed in a better facility.

Here's a link to investigate quality ratings.
https://www.medicare.gov/nursinghomecompare/search.html

Yes, exactly how it should work.

spending down assets is right and legal. Once the assets are exhausted, Medicaid will then pick up the tab once they see that the money was used appropriately.

Yes, self-paying for your own care is absolutely acceptable for future Medicaid eligibility. In fact, Medicaid was designed to provide assistance for people who have exhausted their own resources first. And doing so also has the benefit of improving your sister's chances of remaining at the same assisted living facility after her funds are gone, given that many such facilities will not accept Medicaid's below-market reimbursement rates unless a resident has self-paid for a certain number of months or years. Best wishes for you and your sister.