Amish Friendship Bread starter with buttermilk
Probably not...

Though there are plenty of starters that include dairy, instant mashed potatoes, fruits, etc to inoculate or feed the starter; the goal of any starter culture is to grow and maintain a of yeasts that can efficiently and effectively raise bread, normally wheat or rye-based bread.  Any ingredient added to a starter other than water and wheat/rye, in my opinion, only increases the chances of ruining a perfectly good starter through contamination. The species of yeasts and bacteria that flourish in milk or on fruit may lead to off-flavors.  In cultured buttermilk (widely available in the US) the milk is first pasteurized then inoculated with a mixture of bacteria to produce the tangy flavor and thicker texture.  Unfortunately, this often includes bacteria from the genus Leuconostoc which are known to cause off-flavor in starter cultures and their resultant breads.

On the Other Hand...

Unlike sourdough starters (where a procession of bacteria acidify the mixture to the point where only wild yeast and certain bacteria will happily live there) your buttermilk starter probably has a pH around 4.5.  This is the pH where commercial yeast functions optimally, lower than that (pH 4) the yeast will produce less gas, a lot lower (pH 3) they won't produce any gas at all and may die off.  Refreshing the starter regularly with a mixture of buttermilk and flour provides food for the yeast and helps maintain that optimum pH.

If your friend stopped feeding the starter with the buttermilk mixture and just used a flour &amp; water mixture, I suspect it might stop leavening properly.  As the bacteria from the original buttermilk keep working they will acidify the culture,  over time it could reach a point where the commercial yeast is inhibited, and if it is kept covered in the fridge there probably won't be enough wild yeast to raise the bread.

In conclusion...

If you or the person you plan to share this starter with is likely to feed/refresh it regularly with the buttermilk mixture, then by all means try it out.  If not, you're probably better off just starting a more traditional sourdough starter.  You can always add milk or buttermilk when making dough to get the flavor and texture you want without the risk of contaminating your starter.