On two PCs with a cloud drive (like Dropbox), can I save my QAP settings on this cloud drive?
No, this is not recommended. But there is a better solution.
If you save your settings file (quickaccesspopup.ini) on a cloud drive, you could face synchronisation issues. Let's figure this scenario: 1) you edit your settings on system A but do not save them yet (leaving the Settings window open), 2) then edit your settings on the computer B and save them; 3) finally, back to computer A, you find the Settings window open and Save and Close it. Doing that, you overwrite the changes done on system B and, at best, your cloud drive will show two conflicting versions of your settings file. And there may be other scenarios like this one.
It is a better option to use a Shared menu of type Personal. Then, QAP will monitor changes on the two (or more) computers and will alert you if you have changes on one computer that are not saved on another system.
You can insert your shared menu at the top level of your QAP menu to access it easily. You can also assign a specific keyboard shortcut or mouse button to this menu. Finally, see how user variables can help you if your cloud drive is saved on different root locations on your systems.
More info on shared menus here: Can a submenu be shared on different PCs or by different users?