All household members will have to be listed on the application even the undocumented or individuals who are pending AOS. When snap benefits are granted you will be disqualified from snap case due to non-eligible immigration status. This has no bearing on your AOS because you are not the one who will be receiving the benefits.
When you start working your income will be deemed (percentage), but you still won't be eligible for snap until after 5 years as an LPR.