Can my caregiving services help my grandmother with paying spend down for Medicaid?

It's possible. There are several ways you might get paid something for caretaking your grandmother. First, if your grandmother reimburses you for anything you spend that's directly connected to her See also:
What kind of financial aid programs are available to full-time caregivers? medical care – having to do with her oxygen concentrator, for example – these amounts could count toward the $550 spend-down amount. As for payment to you for actual caregiving, that depends on the specific Medicaid rules in New York (each state does things a little differently). New York Medicaid may permit a certain number of family caregiving hours, calculated at a rate comparable to that of a home care agency aide in your area, to be credited against the spend-down amount. But your grandmother would actually have to pay you, and Medicaid would want proof of the payments. If you do make this kind of arrangement, it might also be a good idea to draw up a simple written "personal care agreement" between you and your grandmother.

Also, some states have a program that allows direct payment to Medicaid recipients for some of their home care. This direct payment program is called Cash and Counseling, or a similar name. The program would pay your grandmother the same amount Medicaid would pay an aide from a home care agency. Your grandmother could then pay you directly for taking care of her. To find out more about these cash assistance programs, go to the page on this site called How to Get Paid for Being Your Parent's Caregiver.

If New York Medicaid would allow direct payment on top of outside, professional home care would depend on the specific Medicaid rules in New Yor (including how much care your grandmother needs and how much for home care Medicaid will pay for any one beneficiary). To find out about whether New York has a direct payment home care program, and whether it works with other home care provided by an outside agency, contact the local Medicaid (social services) office near you.

This was not at all close to my question.