I'm going to update a site from Drupal 6 to Drupal 7. It uses the Views module version 6.x-2.
I would like to know if I need to upgrade the Views module to version 6.x-3 before moving to Drupal 7.
It's not necessary. I have migrated one large site from Drupal6+Views2 to Drupal7+Views3 in just one step.
You have to take in account that views3 (views_ui submodule) depends on ctools. If you follow this path you have to disable views_ui before the upgrade and activate views_ui (and ctools) once the upgrade has finished.
Yes, in this case you should upgrade Views to 3.x first as there is no Views 2.x version for Drupal 7. It might still work to just upgrade Views after Drupal but by upgrading Views first I think you have prepared your site and the upgrade process better.
For more information and checklist on upgrading from Drupal 6 to 7, checkout this link.