The +1/+1 counter won't change how much damage Drana or any other attacking creature with first strike or double strike deals during that combat damage step. However, the +1/+1 counters that are put on attacking creatures without first strike will affect the damage those creatures deal during the regular combat damage step.

Drana's last ability triggers after combat damage has been dealt, so only attacking creatures that survive the combat damage step in which Drana deals combat damage will have +1/+1 counters put on them.