Am I required to have a timer on screen while recording my run?

Nope.

You don't, but I would recommend it as it is fun to customize a live split timer. If you want to, you can look at SmallAnt's tutorial on how to set up your own!

Here is the link:

Thank you both!

I know some people prefer this one by Linkus, as it goes more in depth with various functions of LiveSplit:

Thank you!