Only the touching contact itself is nonlinear. All other assumptions for linear static analysis still hold: small displacement, linear materials, etc. Touching contact in SOL101 uses the same algorithm as used in SOL400. You can find more information on this in the Nastran documentation: MSC Nastran Nonlinear (SOL400) User's Guide
As long as the mismatch in your equilibrium check is small (as it is here), you should be OK. You've already run the model without contact, so you know it's OK for equilibrium and the differences are purely due to the contact.
Only the touching contact itself is nonlinear. All other assumptions for linear static analysis still hold: small displacement, linear materials, etc. Touching contact in SOL101 uses the same algorithm as used in SOL400. You can find more information on this in the Nastran documentation: MSC Nastran Nonlinear (SOL400) User's Guide
As long as the mismatch in your equilibrium check is small (as it is here), you should be OK. You've already run the model without contact, so you know it's OK for equilibrium and the differences are purely due to the contact.