What was peak ITT? The higher the Ng prior to introducing fuel, the more airflow through the engine and therefore greater cooling. Starting the engine with Condition Levers at flight idle could cause an excessive temperature on start. Also, there may have been an accumulation of fuel in the combustion chamber when you engaged the Starter/ Ignition. This can cook an engine.
To answer your questions:
1) Yes, it might
2) Yes
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