That's correct. If current can flow in the loop - that is, the loop is closed somehow - then it does create its own induction and flux. This is called self-induction.
The distribution of the induction differs when the coil creates it, for instance it's stronger near the conductor, so detailed spatial comparison helps little.
Reasoning with the electric circuit helps more. The external field induces a potential difference across the loop. The loop has its own impedance, which includes its self-inductance and possibly other circuit elements. The potential difference divided by the (complex) impedance defines a current. This current tells you what field the loop creates by reaction.