I don't know of a connection at this time. There are "John" and "Henry" Clairs
in my line, but those names were fairly common then. If you find a "Mitchell"
in another group, I'd definitely suspect a connection.

My group moved to Kentucky sometime before 1850. This summarizes the family of that
generation:

Descendants of William T. Clear
1 William T. Clear 1826 -
. +Hannah Asbury 1827 - 1878
... 2 William Leander Clair 1850 - 1923
....... +Sarah E. Campbell 1852 - 1892
... *2nd Wife of William Leander Clair:
....... +Martha Stidham 1871 - 1959
... 2 Mitchell Clair 1852 -
... 2 Columbus Clair 1844 -
... 2 Susan Clair 1848 -
... 2 Thomas Riburn Clair 1856 -
....... +Sophrona Elizabeth Coldiron 1861 -
... 2 America Clair 1858 -

I have a lot more information on descendants, if you think you need it.