The short answer is: No.
Zwift is not ported to these platforms, so it will not run natively under them nor will it run in any emulation that these platforms may offer.
The longer answer is: It's not Zwift's fault.
The Xbox and Playstation (2, 3 and 4) consoles do not support Bluetooth Low Energy (otherwise known as BLE or BTLE), nor do they have support for using an USB ANT+ adapter from any vendor or manufacturer.
Licensing restrictions and partner agreements on both platforms currently prevent the Xbox and the Playstation from supporting a broad range of hardware that can physically be attached to the console's USB ports.
Support for USB devices typically will require drivers and an authentication chip of some sort (think HDCP) built into the device to be recognized and work correctly, otherwise it is treated as a "dumb" HID (input) device such as a keyboard.
This means that while the devices each have fast graphics and each console supports USB ports, they will not allow you to plug in the necessary ANT+ adapter to recognize your trainer or bike's sensors, nor do they support a Bluetooth stack with BLE support to handle Bluetooth sensors or trainers that support that protocol.
Also, Zwift is written to take advantage of OpenGL, an open and free graphics specification. The XBox supports a different engine called "DirectX", which it uses for graphics rendering and performance. This is a Microsoft-only graphics engine. It's VERY unlikely that Microsoft would support porting a competing graphics engine to its own platform, and at a level of performance that rivals their own.
If that wasn't possible, Zwift would have to port the application to both DirectX for Microsoft Windows users and maintain a separate version of the code to support the macOS/OS X and Android userbase who can only use OpenGL. It significantly magnifies the resources needed to keep both versions in feature lockstep at each release.
For now, you can continue to run Zwift on your iOS device, Windows PC or Mac without any issues.