I should clarify that your main RM database probably would not be in Dropbox. Rather, whenever you want to update the RM database on your IOS device, you first COPY your main RM database to a folder at C:\Users\user\Dropbox\Apps\RootsMagic\ where "user" is replaced by the username you use to logon to Windows. I think there may be other ways to do it, but this way works for me.
Then, install the Dropbox app on the IOS device and install the RM app on the IOS device.The Dropbox app will sync the RM database on the IOS device with the RM database in C:\Users\user\Dropbox\Apps\RootsMagic\ The RM app on the IOS device will then use either the most recent copy of the RM database that it knows about or will get a more recent copy from the Dropbox app. The IOS device really doesn't have to be connected to the Internet to use the RM app, provided you are willing for the RM app to use the most recent copy of the RM database that it knows about. There is more than one way to do it, but this is what works best for me.
Your case will be very simple. In my case, I have tens of thousands of files in my Dropbox, and in a certain sense all of those tens of thousands of files sync between my Windows computer and my IOS devices. Except that Dropbox doesn't fully sync all the files it contains with an IOS device like it does with Windows devices. Rather, Dropbox works in a "just in time" mode on IOS, and only does the sync on a one file at a time basis, and only when you try to use the file on the IOS device. Only a very few of those tens of thousands of files in my Dropbox are actually on my IOS device at any one time. So if you are going to be using a Dropbox hosted file on your IOS device, you need to be sure to sync that particular file while you have Internet access, even if later you are going to be using the same file on the IOS device at a time the IOS device does not have Internet access.