What is permissible for a breaker box cover?
Overcurrent protection devices must be Readily Accessible. The NEC defines Accessible as...


  Accessible (as applied to equipment). Admitting close approach; not guarded by locked doors, elevation, or other effective means
  
  Accessible (as applied to wiring methods). Capable of being removed or exposed without damaging the building structure or ﬁnish or
  not permanently closed in by the structure or ﬁnish of the building
  
  Accessible, Readily (Readily Accessible). Capable of being reached quickly for operation, renewal, or inspections without requiring those
  to whom ready access is requisite to climb over or remove obstacles or
  to resort to portable ladders, and so forth.


If you can achieve this with your plan, then it shouldn't be a problem. Keep in mind, however, if you have to remove screws, nails, or other fasteners to access the breakers. This is no longer Readily Accessible.

Also, hiding the panel could be a bad thing if you ever sell the house. So you'd have to find a way to make it obvious that the panel is there, so people can locate it easily if they ever have to access it.

EDIT:

Forgot to mention; as @lqlarry points out, the cover also has to be Fire Rated.