is it necessary to change the model so there are no non-linear supports
No,
CAESAR II will do this for you, that is the purpose of defining the "Static Load Case for Non-Linear Restraints".
CAESAR II looks at the results from this load case and performs the linearization for you. So if a +Y lifted off in the case you select,
CAESAR II will remove it from the model for the dynamic run. If a gap closes,
CAESAR II will take the gap out completely for the dynamic run. If the gap didn't close,
CAESAR II will take out the restraint for the dynamic run.