Probably....It more than likely it is a state program...or county... And it is more than likely there will be a question on form asking about INCOME... You could still get food stamps....keep un-employment and you should try and ask about aid to pay utilities if you are head of household....
In parts of New York State ( could be by county ) you cannot exceed more than $1700.00 per month income in order to receive food stamps. So I would assume they don't care where the income comes from only that you don't exceed the permitted threshold. Call your social services department and ask them so you can be sure. Have a friend call for general information if you aren't up to calling. It's best to be sure of your rights.
When you apply for food stamps, what you do not tell them they will find out, Especially receiving unemployment. The unemployment is accounted for as a income, make sure you bring your utility bills and any daycare information. They take all of this in consideration.