What I mean is: let's say I want to speedrun the CMM, but my friends and I can't (or simply don't want to) play the missions all those hours straight.Can I do it in various sessions and then add the time? Or does it really really have to be in 1 single continuous session?

Main timings use RTA, which is Real Time, meaning if you start the run on 4th January 13:00 and then finish it later, for example at 5th January 15:00 then the run time would be 25 hours. You could submit the In Heist Time as per https://www.speedrun.com/gtao/thread/j8a2t, but honestly only Real Time matters.