If I use a Livesplits timer with segments and I either forget to press the button to go to the next segment will my final time still be valid or do I need to start over? Or is it still valid as long as the final time is recorded from start to finish?

It shouldn't matter. If the timer didn't stop after finishing the game, well, the moderators should check the time when verifying your run, that's it.

you don't even need a timer (unless the rules state it) the splits are more for you anyway ^^ so it doesn't matter if you mess up the splits a bit. The run will need to be recorded though from start to finish per the rules. You also get people who add a timer in post. I would say it should be fine, live split has a button so you can skip a segment if you want to. you can set this button up yourself or use default. hope this helps some sorry if it is confusing :)