No.
Storm
puts copies of the spell on the stack while it counts
spells played this turn. You only played a spell if you announced it, payed the cost and put it on the stack "the normal way". Note that this normally means that only cards on your hand can be played, exceptions are Isochron Scepter and Panoptic Mirror.
Storm
The official rules for the storm ability are as follows:
502.30. Storm
502.30a Storm is a triggered ability that functions while the card is on the stack. "Storm" means "When you play this spell, put a copy of it onto the stack for each other spell that was played before it this turn. If the spell has any targets, you may choose new targets for any number of the copies."
502.30b If a spell has multiple instances of storm, each triggers separately.
The number of copies is set when the storm spell is played. Count only spells that were played (by any player) before the storm spell was played.
The copies are put directly onto the stack -- they aren't played. That means the copies aren't counted by other storm spells played later during the turn.
Each storm spell with a target allows you to change the target for each copy of that spell. You make that choice for each copy individually.
When counting spells played in a turn, you do count spells that were played face down and spells played from zones other than a hand.
A copy of a spell can be countered, just like any other spell, but each copy has to be countered individually. Countering a storm spell won't counter the copies of it.
