The Martian day is about 40 minutes longer than an Earth day. What does NASA intend to do about the Martian day in regards to the Mars mission? Will they adjust the astronauts to their landing day night cycle over the duration of the journey there? Or wait until they land, leaving them on NASA time for the trip, and then adjusting their time to the local day night cycle then? Or ignore the Martian day and keep them on NASA time?
I don't know if planning for a manned Mars mission has progressed to that level of detail yet. I do have some data for the current Mars missions.
For the MER missions, the operations team on Earth initially synchronized their schedules to the Mars sol. This was found to be effective, but uncomfortable as it would disrupt the circadian rhythm (they'd be working nights some of the time). Later on, they went to a sliding schedule that tried to keep in sync while keeping a normal day-night rhythm of the ops team.
The duration of this process and the solar-powered design of the rovers required the teams to work on a schedule synchronized to the Mars clock (1 Mars day = 24 hours 40 minutes). As the mission continued beyond its design lifetime, a combination of team experience and continuing ground tool automation permitted reductions in the process duration, eventually decreasing the number of required handovers. Also, after about Spirit sol 85, MER personnel stopped working a Mars- time schedule and began working a single-shift sliding Earth-time schedule.
For manned missions, this would work in reverse: you don't want the astronauts in situ to keep to Houston's day/night rhythm, so like on the Apollo missions you'd see Mission Control running 3 shifts and the astronauts working in local daylight.
A day length of 24.5 hours is within the body's ability to cope (see experiments where people have to establish a day rhythm without external references, they tend to drift to slightly longer than 24-hour day schedules).