Waross, your analysis is correct. But in reality much before such a stage is reached, the metallic structures near to core will be overheated to such an extent by the over flowing flux, that burning will start. When flux enters metallic parts, eddy loss heat up metal so rapidly that resistivity of metal also goes up reaching a thermal rundown. Copper winding near to core is also affected similarly by overflowing flux. Some of the symptoms of failure from over fluxing in transformers is blistering of painting out side transformers, melting or overheating on tie plate on core, burning of paper covering on copper conductors in winding near to core.
Kakil, To know the time Vs V/F, please refer the Electra paper mentioned in the thread mentioned by waross. You can also have some typical curves of manufacturers in Fig 30 of C37.91- Guide for Transformer Protection. Please note these are all very approximate only and this phenomena cannot be encircled in a straight formula.