Yes, difficulties could occur if the process were not at steady state at the onset of a process reaction curve experiment.  

The process reaction curve method can determine a model between ONE input and an output.  If the process is not initially at steady state, the output is being influenced by some other variable, in addition to the manipulated input, during the transient response.  This combination of inputs would violate the requirement of the graphical method to have a SINGLE step input, and any subsequent calculations could lead to an erroneous model.