Can you operate QB desktop from a company file in dropbox which would make it essentially cloud based?

I would only recommend storing QBD data file on a cloud storage (e.g GDrive, DBox) for the backup purpose. You should download the data file locally anytime you want to work on it, and reupload back to the cloud later. Some of our clients have said that their data files tend to corrupt when opening it direcly to the cloud. 

https://quickbooks.intuit.com/learn-support/en-us/account-management/want-to-use-qb-on-two-computers... 

Yes, I've seen that, but it's just a 3rd party opinion, it's not from QB or even a QB user.

I have come to agree with Fiat Lux. I recently moved to TopBox for cloud storage which automatically syncs from my local hard-drive to the TopBox cloud. I have run, literally, dozens of tests. Quickbooks Desktop cannot open the Company File, not matter how I try to do it. It always fails. I must first copy the file from the cloud to a local drive that is not being linked to the cloud. Do my Quickbooks work. And then, copy the file back to the cloud. In my case, I only copy the QBW file. That file is all that is needed for Quickbooks to open the Company and generate all of the other needed Quickbooks files.