It would not return the same value unless you did it in exactly the same way, or simply observed yourself using the machine such as:
Step 1 (Day 1 - 6:00pm): Jepman hits the random number generator, for the sake of arguement, it returns "59923".
Step 2 (Day 2 - 6:20pm): The Jepman(future) that just did the random number generator goes back in time to watch himself do what he just did 24 hours and 20 minutes ago.
Step 3 (Day 1 - 6:00pm): Jepman is now back in time (Step 1), and watches himself do the process of returning the number "59923" from the random number generator.
Step 3.5 (Day 1 - 7:25pm): Now that Jepman has gone home for dinner, Jepman(future) steps into the time machine and returns to the future!
Step 4 (Day 2 - 6:30pm): Jepman(future) returns from the past, very pleased with how his theory on time travel.
Supposing a time machine did exist, things would happen as they normally would, unless you did something significant enough to change what would normally happen. However, as life itself is very complex, it would be VERY easy to cause a change without realising it.
Such as the classic "winning the lottery" thing, that probably wouldn't work out as great as you thought it would, unless you only travel a very small time frame (24 hours max). Considering you'd have to effectively forget a whole day of your life (since it wouldn't be what happens anymore).
Time travel theory is easy to confuse yourself on, but if you think about things logically and from a "this affects that, that affects this" mindset then it's ok.
Sneaky sneaks. I'm actually a werewolf. Woof.