Cut cord on window A/C
Flexible cords and cables cannot be used in place of house wiring (NEC 400.8(1))  They also cannot pass through walls (NEC 400.8(2)). 

See this answer for more detail.

Cutting the cord also likely voids the UL listing of the product, not to mention the fact that you'll lose GFCI protection. 

Hardwiring the unit would also mean you'd have to reevaluate the overcurrent protection, and possibly increase the breaker and conductor size.  This could also mean that you'd have to remove other outlets (receptacle, lighting, etc.), to reduce the risk of overloading the circuit.