For the standard question of "Can I deploy a Simulink ROS node to _____ hardware?" the answer is usually the same as for "Does _____ hardware support a standard ROS installation?" Most of the time, this means that the hardware's operating system needs to be some flavor of Linux (or Windows/Mac, but most of these questions pertain to Linux) that supports a normal ROS version (and not a version of ROS specially adapted for this hardware). The ROS installation is required prior to deploying the node anyway.
I haven't personally worked with Speedgoat, but from a brief glance, my guess is that it does not support a standard ROS installation. There may be some specialized adaptation of ROS just for Speedgoat hardware. If so, I do not think it would be compatible with deployment of a ROS node from Simulink, though it would presumably work if you manually created the ROS code.
Even if it were to support it, and ROS Toolbox could deploy to it, ROS communication is not guaranteed to be real-time (so you lose much of the benefit of using Speedgoat). ROS 2 has advanced in that capacity by enabling some level of support for DDS back-ends that support real-time communication, but that is not currently usable with MATLAB (as of R2020b).