Atmospheric and oceanic circulatory systems would enable transport of substantial amounts of energy to keep the dark side warmed and the light side cooled to a very significant extent.
The dark side would still become extremely cold and the light side extremely hot by Earth standards but not as extreme as might be imagined. There would be limited life and less ice free water available (the dark side would freeze over) to absorb carbon dioxide. But but with ongoing volcanism still generating carbon dioxide, the atmospheric concentration of carbon dioxide would likely increase creating an enhanced greenhouse effect and warmer air currents.
We don't know for sure how likely it is that bio-genesis will occur on a planet but assuming it did occur as it did on our Earth, bacterial life would spread across the planet before gravitational locking.
Complex life could easily develop in the deep oceans around hydrothermal vents at any time and life in the oceans in general would also be highly likely.
After locking plant life might well evolve in higher latitudes in the more temperate regions between the ice covered terminator and the very hot tropical deserts. And with plant life animal life might also evolve in this area.
During the time before total gravitational locking when the planets rotation was still a different length to it's year, animals and especially marine creatures might be able to migrate and remain in a survivable environment. Annual plants that set seed would also be able to survive extended periods of freezing.
As a partial example of energy transport mechanisms look at the north pole. This spends 6 months of the year in darkness. Although it gets very cold and the sea freezes we do not see cryogenic temperatures because air and water currents such as the gulf stream transport vast quantities of heat energy into the arctic ocean.