The major problem you'll run into with on-prem clients accessing cloud RDBMS instances is the increased latency. The database connections are very chatty, so any increased network latency will be very noticeable with your desktop-based workflows. Some organizations have ExpressRoute links that reduce the latency to a reasonable threshold, but that also adds complexity to the networking side of things.
As a general rule of thumb, I would try a proof of concept where you access the cloud-hosted database from desktop clients and try some typical workflows and see if the increase in transaction times is tolerable.
Another aspect is that if the latency increases (due to ISP routing issues or changes in the network path), technical support cannot help with troubleshooting/identifying the issue since it is expressly discouraged in the documentation. The recommendation is that all components exist within the same datacenter/cloud provider region for the lowest latency and highest chance of success.
Some customers have also implemented a scheduled synchronization of on-prem and cloud enterprise geodatabases, which comes at the expense of lag time before the cloud database is up-to-date, but allows for the hybrid structure you're proposing.
-- Chris Pawlyszyn
