It's reasonably safe; I've noticed some people saying no one should use
rpi-update unless they have a good reason because the kernel is ahead of the standard Raspbian one (and hence, less tested in the field) but I have never had or heard of an actual problem resulting from it.
A potential issue is that Ubuntu updates could then overwrite your newer kernel with an older one, since the practice is to always name these
kernel.img, regardless of version. I don't use Mate, but I do use ARM distros that aren't intended for the Pi at all and hence install useless things in
/boot, creating a similar potential conflict. My solution to that is to mount the first partition on
/boot/BOOT instead (this requires editing
/etc/fstab); that way the distro can put whatever in
/boot, which is now just a regular directory instead of a mount point.
That strategy would make using
rpi-update awkward, so I just copy stuff in from a git clone of the firmware repo (which includes everything
rpi-update installs: the kernel and modules, firmware and device tree stuff in
boot, library stuff in
/opt/vc). Alternately, you could instead leave the first partition completely unmounted (the mount serves no purpose except for updating the contents) except for when you want to access it, or run
raspi-config -- then you would mount it on
/boot, the normal contents of which (the Ubuntu installed stuff) will then be unaccessible, but no harm will befall them. If this is confusing, copy some files into a directory normally used as a mount point, then mount something on it. Notice those files are not there anymore. Unmount and presto -- they are still in the normal directory "underneath" where a device was mounted.
Just remember to unmount after you run the update.