I have an health insurance through my dad on top of my Medicaid and had no problem getting approved.
I have healrh, dental and vision insurance through work but I was still approved for Medicaid. It goes by income, not current coverage so that's expecially helpful if you're like me and are having a really hard time working because of fatigue and such. They will access or request your pay stubs to go off of what you are really making in a pay period. Also, if you qualify for Medicaid you automatically qualify for WIC :)
Yup you will be approved I also had health and dental already but was still approved, because I couldn't afford the copays of my primary insurance.