In my opinion adding a supertweeter can be detrimental if the speaker sounds balanced as is. If you're augmenting with a subwoofer or if the speaker has very good bass but could use a bit more energy on top, then a supertweeter will help.In any event, a supertweeter will probably improve the detail and sense of speed. In my opinion those characteristics are nice if they don't come at the expense of making the tonal balance seem too lightweight.
I use or have used Fostex FT17H and/or T90A with an equalized FE206E, which was augmented down south by a powered woofer section. Without the augmenting woofer, the equalized FE206E sounds more balanced to my ears without a supertweeter.
Duke