Yes, it is possible to edit just about anything on the JV-1080 from the computer using SysEx messages. Programs that are made to do just that are called Patch Editors. Here are a few patch editors that will work for the JV-1080.
WinJV - freeware
OSC-1 - freeware analog synth style editor
UNITY 2080 - $65 shareware
JVEdit - $? shareware
Unisyn - expensive commercial software by MOTU (more expensive doesn't mean better in this case)
Mitch
The Sonic Spot