No, counting on the hands is not base anything, because positional number systems did not exist. Just like Roman numerals or tally marks aren't base anything.

No, counting on the hands is not base anything, because positional number systems did not exist. Just like Roman numerals or tally marks aren't base anything. People counted on fingers like with tally marks - they could express the numbers one through ten. Thus ten became an important and familiar number to humans. Thus it would have seemed natural to use a base 10 number system many millennia later.