I own it and I can confirm that it works perfectly in Linux and openSUSE.
As john_hudson stated, you have to install the hplip packages.
I connect it via wireless network without any problem.
Printer, fax and scanner are perfectly recognised.
The installation is pretty simple: run the hp-setup command from CLI and follow the instructions on the screen.
In general hplip is very well supported in Linux.
It even has its own site: https://launchpad.net/hplip
I may have picked the wrong HP OfficeJet Pro 8600 variant. This here may be your contemplated printer instead: HP Officejet Pro 8600 E-aio n911a where I note that is also reported as working with openSUSE.