Migrate SharePoint 2010 sites to SharePoint online (migrate the sites as-is)

john john yes your understanding is correct.

If not mistaken you can request a 30d trial license to test the software (this will give you the possibility to make some tests).

The "beauty" of ShareGate is that will detect all dependencies needed for the destination site and it will automatically try to import all the needed objects when attempting a SP to SP migration.

In terms of tool, I personally believe is one of the best for this kind of activities.

I know the free migration tool from Microsoft (SPMT) got enhanced and it may work for some migration scenario.