"Is there any reason this will not work?"
You will have a couple of issues. Mostly, that device is really slow, compared to the local harddrive, for the relational database and the associated utility files that are Live Updated while you work. This is not like Word or Excel, in that the file is not Loaded into local memory while you work.
"I will use a cloud service to backup the hard drive. "
That also isn't good enough. What you would do is use the QB function to make a backup file (.qbb) and you can make that to the external device. Then, the Cloud will mirror the .qbb. The .qbb is your safekeeping and disaster recovery file.