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.
UMMMMMMMmmm no.
It STATES it was at the time of DAVID go to the site posted in #13 and read it.
“What he has found so far has impressed many. Two burned olive pits found at the site have been tested for carbon-14 at Oxford University and were found to date from between 1050 and 970 B.C., exactly when most chronologies place David as king. Two more pits are still to be tested.”