Not 12 second to lift off, but from 80kts on all new caution alerts are suppressed (until 400ft) and from 100kts all new warning alerts (until 50 ft) so that is the main issue.
PWS is activated by thrust lever angle above a certain value (53°?) if weather radar is not selected active before that. It even begins to scan if only the TLA is above the required threshold, doesn't matter if IRSs are aligned or engines are off.