The site is not completely unearthed, and it has been established to BE at the time of David.
Check my previous post for more info.
Um, no.
The site has been established by radiocarbon to date plus or minus 50 years of the date the currently dominant chronology assigns to David; the pottery shard was found in a fill at the site, establishing its own date as presumably older, but by an unknown amount.
Calling the site Davidic begs the central question of the reliability of the current chronology.