Can I upgrade desktop software on a Server without negatively impacting the server software?

[AnnVanSlembrouck]

I plan to upgrade the desktop software from 10.3.1 to 10.4.1 prior to upgrading ArcGIS for Server from 10.3.1 to 10.4.1

Is this the proper protocol for a server?

[JoeBorgione]

I think you'll be okay:

Client and geodatabase compatibility—ArcGIS Help | ArcGIS for Desktop 

[AnnVanSlembrouck]

Thanks Joe. The link you provided speaks to the compatability of client and the version of the geodatabase

My questions is referring to upgrading the desktop software prior to the server software when they both reside on the server.

[JoeBorgione]

Oohhhh... Oops; running two versions on the same box....  Not sure about that.  Sorry. You might do well by calling tech support for that one....

[JayantaPoddar]

You can upgrade the the ArcGIS Desktop/Server in any order.

My suggestion would be to do the upgrade when the traffic in the ArcGIS Server is least (Before start of the day's working time or at the end of it), to avoid any issue that arises during upgrade. Also remember if you are using web-adaptor, you need to unregister/uninstall the older one and install the new instance.

[AnnVanSlembrouck]

Thanks Jayanta!