Is it a good idea to connect a line buffer to ground?

You should always tie unused inputs to a valid logic level. That could be tied to GND or to the VDD voltage rail. Never leave unused inputs floating in that it can cause excessive power dissipation in that IC package and introduce extra noise into the voltage / GND rails.

It is common practice to use a pullup or pulldown on the unused inputs on unused gates. This makes it easy to use the gate if it is ever needed for a design re-work on the board. It gives an access point to connect to the gate and prevents having to cut an input loose from a voltage or ground connection.

With any CMOS logic IC, you MUST connect unused logic inputs to a known logic level. You may connect unused inputs to either High or Low, whicever is convenient (or whichever is necessary to make the part work as desired).

An unconnected CMOS input may take on any level - if it sits at a "maybe" state, the input circuit will draw excessive current, and may damage the chip.