Pedal strike will absolutely be an issue. If you have the bike already, measure off a 20" wheel on your existing wheels, and visually check how close the pedal will be to the ground.
Most mini-velos have unusual frame shapes that place the axles lower, you can't just fit smaller wheels to a larger frame and make a minivelo. Are you able to do structural welding ?
Your other problem will be brakes - a disk brake would help a lot here, rim brakes will not work at all given the different rim positions.
Notice on this example that the rear axle is below the BB, so the chainstay slopes down toward the back. A larger bike has a horizontal chainstay, or full sized road bikes slope up from BB to the rear axle.