No, You Won't Have Any Problem What So Ever.
Asylees & Refugees Are The Only Categories Eligible For Welfare.
1. Only Asylees Are Eligible For Welfare, That Has No Effect What So Ever On His Adjusment Of Status, Or Application For Future Citizenship.
2.unemployement Insurance Is Not Welfare Is Not Public Assistance It Is More Like A Preminium You Are Buying Through An Insurance Company In Case You Loose Your Job You Can Collect Some Money On A Wekly Basis.
You Will Be Fine.