Yes. "Greasing of the Windings" can case many different types of problems (some short term, some long term) but ultimately can result in failure if the issue is severe or compounded by other issues or operational conditions:
1) It can affect heat shedding in the windings, attract dirt and block...
I have a 2500kVA, 13.8V:600V, phase config. Dyn1, dry type transformer supplied on the primary side via separable insulated connectors (insulated elbows and bushings). The connectors are the plug in type as opposed to the bolt on type and therefore rely upon the spring tension of the bushing...