Class II isolated power supply (wall wart) -- referencing the output to mains neutral?
It should not cause any extra hazards or problems that I can think of, beyond the output being 'live'. However there are potentially serious consequences to the output being live- see below. 

Typically the output (-) is AC-connected to the neutral anyway, but galvanic isolation provides safety and the capacitor is extremely high reliability high-voltage Y-type capacitor because a direct connection (what you want to do) is potentially fatal in general purpose applications.  

Keep in mind that the cord will not typically be rated for mains voltage and that will have to be dealt with. If it's all in a box and the cord is sleeved with approved sleeving, and the connector cut off, it may be okay. 

If you're planning on powering a device connected to the mains with a wall wart actually plugged into a wall (rather than locked in a box) or with the original barrel connector and/or cord still attached no, don't do it. 

Here, for example,



is a cord connected to a 9V "wall wart" that has sustained damage from a desk chair running over the cord. As you can see, the "live" wire is exposed and ready to shock someone were it not to be isolated. Same thing applies to the barrel connectors- they are not designed to be shock-proof.