The 400 Series cameras (D415 and D435) work with any Intel or ARM processor and just need a USB 3.0 port. So since Odroid has an ARM processor and 2 USB 3.0 ports, it should be fine with the D435.
In regard to Ubuntu MATE: it is the first time I have heard of this OS. I would speculate that the generic version of Ubuntu MATE would have the best chance of working, rather than the one optimized for Raspberry Pi.
This OS requires ARMv7 architecture, which the Odroid XU4's ARM Cortex-A15 apparently has.
It is important to note that the RealSense SDK 2.0 software recommends Ubuntu 14 / 16.04 LTS. So I culd not give a guarantee that it would work with Ubuntu MATE.