Is there a way to download tracks from inReach Explorer+ without an inReach account?

AFAIK, the only way to get anything off of an Explorer+ is via the Explore web site, which does require an account. This is true of every inReach device up until the 66i/86i series, which allow you to mount the device as a removable USB "disk drive".

And yes, this does (to some degree) bang heads with the idea that you can use the device "unactivated".

The lowest cost approach is probably to start a Safety plan (the lowest cost plan) as Freedom plan (rather than annual). Then suspend it as soon as possible. You should still have access to the web site and functionality even though the plan is suspended. That should include the ability to sync the device, which is what is required to get the logged track points track to the web site. You will, however, have to pay the annual fee to keep the Freedom plan. 

Note that I have never actually TRIED this. You should probably call tech support to be sure that my assumption about the ability to sync with a suspended plan is correct.