George, I write from the perspective of someone who uses a 1+ fret regularly in my own playing. I have dulcimers without it, but I use them mainly for teaching, since beginners get confused when my fretboard does not look like theirs.
If you have vintage dulcimers of any monetary or historic value, I would not add the extra fret. But feel free to add it to modern dulcimers or those whose values you don't er . . . uh . . . value.
You ask what notes you get. Obviously the answer to that question depends on the tuning. In a DAd tuning, you get the lowered (or minor) third (meaning an F natural) on the bass and melody string and you get the 7th (meaning a C natural) on the middle string. Just being able to play a 7th chord down low without jumping up to the 6th fret is really nice. And the lowered third of the D chord is also the 7th of the G chord, so you get D7 and G7 very easily. With that C natural, you can also play a C chord, which is found not only in modern music but also traditional tunes such as Old Joe Clark, Red-Haired Boy, Salt Creek, and more. I often use the 1+ fret on the melody and bass string just to add a little bluesy sumpin in the middle of a short solo, but it also allows you to play the minor pentatonic scale, so you really can play the blues in D without a capo and without retuning. And of course, you get the entire D minor scale as well.
We should really create a discussion in the Extra Frets group about why people like the 1+ fret.
Dusty T., Northern California
"A good song makes you laugh, it makes you cry, it makes you think."
-- Pete Seeger