Using a red pen to annotate your thesis can be useful. Underlining typos, circling important things, boxing off ideas.
Using a red pen also carries a lot of negative associations. Crosses in the margins of tests or essays in the past, a circled grade, a short note that diminishes effort.
Annotating your thesis is essential for viva prep. Using a red pen is not. Choose your tools. Think ahead a little for what you will need and what you can do to make the process effective and your annotated thesis useful.