Ahhh... first post didn't say you already had Steam...
But yes, you can use JSGME, it will work fine with the Steam version. After all, the JSGME stands for "JoneSoft Generic Mod Enabler". It will work with a lot of games, especially the older ones -BUT- do not put the game itself into a "Program Files" folder, still. Steam can present additional problems with its Steam Library folder paradigm. See
Moving a Steam Installation and Games for some background. You have to set the path to a folder of your own making while installing Steam, if you only have one hard drive... The Steam version can usually be copied to other game folders just as easily as other version, so that you can use multiple mods while using MultiSH4 and a unique Save folder name with each.