It depends on your definition of "work" and which Yongnuo triggers.

If you are thinking of the "manual" triggers (RF-602, RF-603, RF-603II, RF-605), then yes, they will work, but all they can do is trigger the flash with correct timing. You won't have any of the other features that are probably why you're paying extra for a TTL-capable Metz flash.

If you are thinking of the TTL triggers (YN-622N), then yes, they will work not only to fire the flash, but also with FP/HSS (if you end up upgrading to a body that can do that--the D5200 can't), 2nd curtain, and iTTL. However, the interface for power control and groups is nonintuitive with only LEDs to indicate the state of the flash, and you might prefer a YN-622N-TX dedicated transmitter on the camera (the LCD display and buttons make some things much simpler) if you want to explicitly set the flash's manual power level from the camera.

Regardless of which system you go for, you will need a radio receiver unit for the flash itself, and another transmitter unit for the camera. Yongnuo triggers are radio-based, and the Metz has no built-in radio receiver--only an optical slave sensor for CLS and a "dumb" optical slave mode.