TL;DR: It'll turn, but not well. The two fixed wheels on one side will act against any turning moment you attempt to apply.
As others have mentioned, having your fixed wheels on a common axis, like on the zero-turn mower, is much easier. Think of a shopping cart, or a wheelchair, and how it's configured. Casters up front, fixed wheels in the back, right? I spent a couple years working as a loader and cart wrangler at a home improvement store and got to understanding their behavior quite well. They're happiest when their center of mass is ahead of the axis on which the fixed wheels rotate. Basically, the axle you'd put the bearings on. That axis, when extended to infinity, is always going to have the point around which the cart/car/vehicle/etc. turns on it. And it will naturally seek to keep that axis behind the center of mass. That's where it's dynamically stable. IF you reverse it, and put the axis of the fixed wheels ahead of the center of mass, like pushing a cart from the nose/front, it's unstable, and will flip around if disturbed by even the slightest amount. Different friction levels in the fixed wheels, a bump, a gust of wind, etc, and it'll gleefully whip around and put the casters forwards.
What you're proposing takes your fixed wheels and puts them on two separate axes. This is going to provide a very strong stabilizing force. Think about how the axles on a big semi truck are set up. Yes, it's mainly for load distribution and reducing footprint pressure, but it also provides some extra stability to have the multiple axles in parallel like that.
If you've got two motors, and two steering servers, which is what I'm understanding your situation is, you'd be much better served by putting both motors at the back, both steering servos at the front, and having a mode where you can basically turn both wheels nose in if you want to turn really sharply, then drive the motors in opposite directions.