I'll be able to dock with mules, battle autons and my wingmen, and fly them to a dock like my own ship
That's right. As for how your ship behaves when you aren't flying it, that depends on your ship, but will probably be quite simplistic.
sort of like the Playership Drones mod?
sort of.
I haven't actually tried Playership Drones, but from what I gather it requires your ship have docking ports and be set up for independent operation (communications element, aisettings, etc). Your old ship will behave like a drone when you switch, but not all (modded) ships are compatible. I may not be entirely correct here.
UGW operates on the assumption your original ship does not meet any particular standards at all. Consequently you can always get back to your original ship by pressing u twice to invoke an item on the new one, provided the ship still exists (possible bug here, i have an idea to fix it), but your original ship will most likely exhibit very basic ai when you are not flying it, following your new ship unwilling to take any orders including "wait".
It assumes you won't be spending longer in your other ships than you need to for the upgrades.
A bit of advice: Mules can indeed accept weapons, but get themselves killed with anything that isn't omni. A heavily armored mule with an im90 is a force to be reckoned with, able to help you in combat against weaker foes. On the other hand a heavily armored mule in sanctuary with an omni laser will do little more than draw enemy fire to itself and get itself killed.
