Can the air flow meter be removed when installing a cold air intake?

It can, but your engine will not run properly. My advice would be to put the sensor in between the air filter and the throttle body. This is straight from wikipedia:

An air flow meter is used in some cars to measure the quantity of air going to the engine. In the case of a gasoline engine the electronic control unit then calculates how much fuel is needed to inject into the cylinder ports.

The vane (flap) type air flow meters (Bosch L-Jetronic and early Motronic EFI systems or Hitachi) actually measure air volume, whereas the later "hot wire" and "hot film" air flow meters measure speed of air flow.