When we talk about the Migration to Magento v2.x, we mean Magento data migration and M2E Pro data migration. These are two different processes that should be performed separately.
Magento migration goes first. At this stage, all M2E Pro tables should be ignored in order not to be moved along with Magento data. Right after your Magento data is fully transferred, you can start migrating your M2E Pro.
When you launch M2E Pro data migration (see Step 1 of the Migration Guide), M2E Pro on Magento v1.x becomes disabled, all updating processes completely stop. It is done intentionally, with the purpose to eliminate the issues of double data synchronization from both M2E Pro on Magento v1.x and Magento v2.x after the switch.
M2E Pro Migration tool will automatically prepare the Module database on Magento v1.x for the migration. All the data will be saved, including your Channel Sales, Product and Order logs, Scheduled and In Progress actions, M2E Pro Accounts, Policies, Listings, and other configurations. It can take up to 15 minutes to complete the process. Then, you need to create a dump of the M2E Pro database in Magento v1.x (see Step 2 of the Migration Guide).
After you move the Module database dump from Magento v1.x to Magento v2.x, the Migration Tool will unpack and validate it automatically. All Identifiers (Products, Orders, Attributes/Attribute Sets, Website/Store View, etc.) from the M2E Pro Magento v1.x database will be adapted to the Magento v2.x environment.
Once you complete the Migration Wizard, you can start using your M2E Pro on Magento v2.x (see Step 3 of the Migration Guide).