No, if your license if revoked in Kansas then you will not be able to obtain an Ohio driver's license. According to the Ohio Digest of Motor Vehicle Laws, under OH law no driver's license or temporary instruction permit may be issued to any person who is under suspension or revocation from Ohio or any other state.
Ohio and every other state within the United States checks the National Driver Register (NDR) to find out if a person is listed there as a problem driver such as one that has any suspensions, revocations, license cancellations, etc. So even if you failed to tell the Ohio Bureau of Motor Vehicles (BMV) about your KS license being revoked they should find it out when they check the NDR when you apply for a license.
Normally to get a new license in a new state you will need to take care of any issues in your previous state with regards to your driver's license. You can contact the OH BMV to see if there is any way in which to receive an Ohio driver's license. Typically a state will require that you take care of the Kansas issues and get that license reinstated before you can obtain a new license.
If you are able to get an Ohio license you can get instant car insurance quotes here with us so that your vehicle is properly covered.