Is it possible in a recording to stop the game together with the timer and then continue from where you left off or that is not allowed?
Most games do not allow to stop the timer for any reason except a reset or the run is finished. You can pause the game, but you need to leave the timer running. Some games have categories or special rules for some categories that allow breaks/pauses, but those are a case by case basis. You need to check the rules for each game/category you want to run to see what is allowed and what isn't allowed.
What you describe is exceptionally uncommon except for extremely long categories (like 15-20+ hours long), and even then it's far from a sure thing. Now bear in mind, the rules for the leaderboard here only (in all likelihood) keep you from submitting your runs to that leaderboard. Nothing stops you from speedrunning however you please for your own enjoyment.