If the EGR valve is inoperative, your check engine light should be on. The EGR valve recirculates exhaust gasses back into the engine to lower the combustion temperatures to minimize NOX emissions.
There are numerous reasons why a vehicle "burns a lot of gas."
State of tune, restricted air filter, fuel pressure, faulty O2 sensor(s), low tire pressures, sticky brakes, congested city driving or excessive idling and so forth.