Does Linux support storage device without driver?
Yes, USB masstorage is suported MTP also
But think of that when in USB Masstorage mode watch need to unmount the filesystem and remount when cable is disconnected but your engineers probably know this, the downside is that if you charge during training you don't want to enter this mode, I don't know if you can detect a "charge" without entering a USB Masstorage mode this is a question for your HW people. If you use MTP you don't have there problems.
All systems worth mentioning support USB mass storage.
The USB Host protocol can be implemented in smartphones/tablets too (Andoid in 3.1+ has support, not much HW supports it). I am sure that there will be competent smartphone applications (I like Activities Viewer for Android), but in that case I want the main database somewhere else. Just converting the Globalsat binary to well known xml conversion can be implemented in a portable way, so it can be done in smartphones and websites.
..and for charging: If it is OK to connect just the USB power, not data, to get a unit working normally and charge, it would be sufficient for me.
I have such a cable to charge my phone from a USB charger. If I use a standard USB cable, the device charges much slower.
If I do not have to turn on the device when loading data, I do not have to turn it off afterwards. It has happened a couple of times that I have forgotten that. With the 625XT no damage is done due to excellent battery life.
Also: A waterproof USB micro contact would simplify connecting the device.