Actually, yes. Don't you? It is your job, it is clearly defined in your company manual, it is expected by the FAA, and is owed to each and every pax in back. Let me guess, your one of those guys that does 25 minute turns right? You know the ones.... the CA looked at the AML so I don't have to.... the FO programmed the FMS, so I don't have to check it...

Our tasks are clearly defined, if that results in delayed departure times, then they will have to add more time to perform all the required crew functions and duties.

Frankly I was a bit surprised by this thread. This partial reading and glossing over is the stuff that leads to accidents/incidents and violations.
It is not the mark of a professional and the fact that it apparently is happening is concerning.

To answer your question. Yes, I do review the entire release, to include notams. Flying since 1983.... 25 accident/incident and violation free years. Can I do all my tasks in a 25 minute turn... yes.... but that leaves no time for a restroom call, snack break or other human issues. If any of the above happen, and it was a 25 minute turn, then it goes out late. Safety is our number one responsibility... not on time departures.