I'm not sure you will find someone who has had the experience you are asking about. I am not up to date on the numbers, but you could compare what the stipend is with the poverty line for your family size. If you are below it (and you aren't disqualified for being in school-that is a question some people might have an answer to, can you qualify for benefits if you are a student?) shouldn't be a problem. If it is above it then the question would be what types of income do they count for qualifying for those benefits. Scholarships aren't included, but your stipend would be a wage I think which would count.
Edit-found this info for California, other states may have a similar rule, but you have dependents so I guess it wouldn't matter.
All able-bodied persons (ages 18-49) without dependents must work 20 hours per week (monthly average 80 hours) or participate 20 hours per week in an approved work activity or do workfare. If not, these persons receive only 3 months of CalFresh benefits in a 36-month period. There are some exceptions, so contact your local County Welfare Department to find out if you are eligible.