I'm not sure. Is there a reason it wouldn't be safe? It's fine on Raspbian but I've never used Ubuntu MATE on a Pi, so maybe there's a specific reason not to do it that I'm unaware of?
In doubt, run the dist-upgrade command without the -y option that you used in your original command and you'll see the list of packages that will be installed/updated before being asked to confirm (or cancel).
But if the current versions of your packages can't be updated because of new dependancies, you won't be able to do it with a simple apt-get upgrade.