Yes, your combustion will be less efficient, therefore rising the EGT.
Tu engine needs more fuel to run at the same speed. If the engine is running at full speed, you will damage it.
FOD guards made by wren are really nice, ,since there is no airflow restriction. The mesh is larger than the air intake of the turbine.
An other problem that can be met with custom made FOD guard is when the mesh is too close the the compressor wheel.
Specially true on small turbines, the airflow can be disturbed causing the compressor wheel to cavitate.