I would say no.
However if the deflection is so small that it falls in small strain then you could use linear elastic material as a substitute for hyperelastic material. Generally hyperelastic materials are used with large strains so we must use a hyperelastic material definition and the required large deformation option.
Even if a material is typically classified with a special behavior (like hyperelastic) does not mean that other, even simpler material models can never be used.
On occasion I have even seen large deformation solve faster, but generally you are correct, if large strain is not needed then turning it off will save time.
There can be some improvements to solve times by careful modelling. What makes solve take really long and fail is often due to distorted elements under large strains. Even though you might think fewer elements would solve faster sometimes significant improvements can be made with finer meshes in the areas of large strain so the element distortion is lower. Also watch out for snap-through conditions and turn that on when needed. (arc solver) Even with snap-through on, some problems will still challenge Creo to solve. A small part of why is the P-elements used by CREO. Although often more accurate, this accuracy can cause problems like singularities that do not show up as much in H-element codes. For one, H-elements tend to average stress/strain much more than p-elements. Contacts are generally more math intense in P-elements as well.
