Tormek's sharpennig guide to turning tools has this to say
"Influence of heat on HSS steel
HSS steel can stand a much higher temperature than carbon steel without decreasing
the hardness. However, at the very tip of the edge, which is very thin, the temperature
can easily rise to a level which will affect the hardness. Therefore grind cautiously at the
tip of the edge and do not allow it to become blue. Overheating HSS steel can cause a
decrease in the hardness by as much as 4 HRC, which shortens the life of the edge. If
you cool it in water, do not cool abruptly from a high temperature, since this can cause
micro cracks invisible to the naked eye."
which is pretty consistent with what you have outlined -
1. you may soften an edge (short term) but you won't kill it.
2. not a whole lot to gain from quenching - and some risks associated.