I'm not familiar with that particular application, but I would think that it depends on what you're doing. As a general rule-- yes, it should be perfectly safe. The only "danger" would be if something went wrong while the backup were being made or restored. Also, you wouldn't want to restore an old backup and lose all of your latest progress.
I use Dropbox as one of my cloud services, and I chose to install Arena within my Dropbox folder-- inside my "Dropbox" folder is a folder named "dosgames," and then inside that folder are "ARENA" (with its subfolders) and "Daggerfall" (which I haven't actually installed yet but the installation package is in there). I mount the "Dropbox\dosgames" folder as the "C" drive in DOSBox-- which is not installed inside Dropbox-- and then I run Arena from there. That way I can play Arena on my desktop computer in my bedroom, and then if I'm traveling-- or just sitting in front of the TV in the living room-- I can continue playing Arena on my laptop computer without having to copy any files manually, since Dropbox keeps everything updated and synced automatically. Or, if for some reason I'm stuck somewhere without internet, I can play "offline" and then let Dropbox update my desktop from my laptop once I've got an internet connection again.
I even set everything up so I can launch Arena from within Steam.
EDIT: I forgot to add that I have had a few occasional glitches when saving a game in Arena, but I'm not sure if they were due to problems with Arena, with DOSBox, with Dropbox, or maybe with something else. Basically, I would save a game just before doing something potentially dangerous (like resting in a dungeon corridor to try to regain some hit points when I was close to death), and if I needed to restore I might find out that the game was corrupted and couldn't be restored. When I looked at the Windows "command prompt" window I would see that there was an error message when Arena was trying to write one of the files. So now I position the "command prompt" window such that it's sticking out to the left of the Arena game window, so that when I save a game I can glance over and make sure the files were written successfully. If I see an error message, I save the game again so I know the files got written okay.