What's the file format on the thumb drive?
If FAT32 then that format cannot handle files larger than 4GB.
Do I even need to back this up, or will I always be able to download it from the Adobe site?
I definitely recommend keeping your own backups of any files that you purchase - from Adobe or anywhere else.
There is no guarantee that the file will be available for download at a later date when you want it.
One of the most frequent questions on this very forum is how to download previous versions of Adobe software since Adobe's habit is to remove public links to previous versions from their website as soon as a new version comes along. This frustrates people no end but there has been no change in Adobe policy.