No. The engines cut out (four of them) because of the final heavy list of apx >40°.
After the initial violent list, the ship then righted itself to apx 15°, which enabled many of the survivors to have a ten-minute window of escape, [the JAIC does not mention this at all] before it lurched to 45° this time cutting off the engine completely. In other words, the first lurch following a bang or series of bangs or feelings of a collision, were followed by a frantic attempt to get dressed and/or run up to the upper decks, some not even bothering to dress. This fits the reported timings of 0100 and the final fatal list circa ten to fifteen minutes later.
The people who did not do this were likely doomed.
Attached is the direction the vessel turned, according to the JAIC, basing its timing on Treu's testimony.