I am pleased to report that Origin Pro 2017 works beautifully on Linux. I am using the 64-bit version of Origin Pro 2017 in a Windows 10 64-bit bottle with Crossover for Linux 16.2.0. My linux version is Linux Mint 17.3 64-bit with the Xfce desktop. This version of Mint is based on Ubuntu 14.04 64-bit LTS.
I have not yet done exhaustive testing, but the Origin Pro 2017 interface looks exactly as it does on a dedicated Windows machine, and I am able to enter data, plot and revise a graph, do a linear fit to the data, and print the completed graph. I can also access the link to add-on apps from within Origin Pro, and I am able install and run these apps.
Origin Pro 2017 has links or consoles for external programs such as Mathematica, Matlab, and R. Naturally, these links will not work with linux versions of these external programs -- they would have to be Windows versions. It might be possible to link to them in a separate Windows machine or VM, but I have not tried this.