I understand that the turbine of the engine runs the compressor and the fan of the engine. If the air flows through the compressor undisturbed, can we avoid having an inlet in the gas turbine engine to reduce drag of an aircraft?
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If you are talking about the inlet (diffuser), this is not a good idea for several reasons
UNIFORMITY OF AIRFLOW THROUGH THE ENGINE
Because of the design of the diffuser, it can eliminate turbulent airflow and, in the case of supersonic aircraft prevent the engine from ingesting shockwaves, causing compressor stalls and flameouts. Diffusers also direct the air into the compressor in a uniform fashion, reducing engine problems if the aircraft is sideslipped or at high angles of attack.
ADDITIONAL RAM AIR COMPRESSION
The diffuser can provide additional compression at higher speeds vis a vis ram air forced through the diffuser slowing it down and compressing it. While this process does create additional aerodynamic drag, it provides the engine with denser air to use and subsequently more thrust.
RCS REDUCTION FOR MILITARY APPLICATIONS
Jet engine compressors and fans are strong radar reflectors, which increase the radar cross section (RCS) of an aircraft. Diffusers can be designed to either hide the engine compressor from view of a radar using a S-shape diffuser or cover the diffuser inlet with a grill having openings narrower than the wavelength of a potential radar beam, much like the grill on a microwave window protects the people around it.