I cannot help you much with Ubuntu, other than to warn you about the differences between Window's name resolution, versus Ubuntu's, which I'm sure you are well aware of - but the game itself, and most mods have file and folder names that are not identical. In windows of course, "Data" resolves the same as "data", and it doesn't matter. But in Ubuntu, "Data" is different from "data"... so you'll have to inspect your game and the mods, and be certain the names are the same. That said, if you have the game already running fine in Ubuntu, then adding mods with JSGME should be fine, other than as I mentioned, the names...
Some Threads:
JSGME on Linux/Wine - 4 years old
SH3 Resolution Fix under Linux/Wine - BarracudaUAK posts in this one
SH4 on Steam, Running Linux/WNE - by BarracudaUAK
Let's Install Linux on Moonlight's Spare Computer! - by Rockin Robbins
I don't know if any of those threads can help you, but certainly some good reading. Both Barracudo and RR are busy, but PM them also if you need more help. SH3 is not exactly the same as SH4, but they are very closely related.
