Synergy Needs a GUI
Synergy (see also here) lets you "join" up multiple desktop interfaces on different machines, letting you treat them as though they were different screens on the same machine (even though they are not). You can use the same keyboard and mouse for each.
If you use arrow keys to control your mouse pointer, that shouldn't be a problem for Synergy.
However, Synergy will only work on machines that have desktop interfaces running.
If a server system has a mouse pointer (even from an attached mouse) but it has no GUI running, Synergy will not work. (And it wouldn't make sense for it to work. If you want a console to operate seamlessly as part of a single GUI, just SSH in to the server from the desktop machine.)
Web searches for
synergy "command-line only" and similar strings return results because the Synergy client executable (for some OSes) is a command-line-only executable--that is, it doesn't have its own GUI.
To verify to a reasonable degree of sureness that Synergy requires a GUI to be running, I consulted its source code. In this file, you can see that a host's operating system determines if the
CScreen object is instantiated from the
COSXScreen subclases. X Windows is the GUI in most Unix-like systems, including all GNU/Linux systems (which includes Ubuntu). You may have heard of it referred to as X11 (which is the most common of its several names).
While that doesn't rigorously prove that a Synergy screen on an Ubuntu machine needs to have a GUI running, it constitutes significant confirming evidence to an otherwise consistent understanding of what Synergy does and does not do, which I believe to be cogent.
A Server Can Have a GUI
I said Synergy won't work if a GUI isn't running. But an Ubuntu Server system can run a GUI:
On the other hand there are some good reasons to avoid installing and using a GUI on a production server system (see also this part of the ServerGUI page).
If your Ubuntu Server system has a GUI running, Synergy should work fine. (Similarly, if you have an Ubuntu desktop system with no GUI--equally possible--Synergy will not work.)