I do something like this, but with Owncloud/Nextcloud rather than dropbox.
In theory, things should I think be fine - but I have hit occasional problems and TBH I am not convinced that things are seamless. I don't find the prompts that Leo gives when it detects this kind of thing very helpful, and I have hit what seems (to me) be be occasional mis-syncs. Usually this is related to 'derived' files using @file etc. I have another, more standard, file editor that I use in a similar way (for a daily diary file), and that seems to be pretty solid.
It is possible that my problems are caused by use of both Windows and Linux machines, and the way timezones are setup differently on some of my machines.
Edward has given some pointers on the general 'reloading from disk' etc. situation in the past, but like I say, it has never seemed quite solid to me. My current workflow is basically to ensure I am only editing on one machine at a time. This is liveable-with for me ATM, but I would like to have more confidence in the general setup.
I would appreciate more input from others on this topic.
Jon N