Based on the tournament rules, you only need to agree on the storm count when the game calls on you to know it to correctly perform a game action, so you have no obligation to correct your opponent before then, though you are not allowed to lie about it, either. Murgatroid's answer explains the details.
However, note that any confusion or disagreement is likely to require calling a judge, and that judge is likely to end up having to stand there and reconstruct the entire turn to figure out the correct count — something that can be fiendishly complicated if, for example, a Past in Flames was played as part of the combo.
So, practically speaking, this is going to be a headache for everyone involved. You're also at a disadvantage: your opponent might argue that you previously agree to their count when they incremented the number and you didn't dispute it. So you will want clear evidence to convince the judge that your version of events is correct.
In short, this move is legal, but you need to also think about it in practical terms, since you're entering a procedural quagmire:
- If you're going to choose to wait til the last possible moment to dispute the storm count, you should keep impeccable notes. This will help ensure that you get a correct ruling, and quickly.
- Even with the best intentions and utmost preparation, your peers may regard it as unsportsmanlike, since you're choosing to take one of the most annoying aspects of the game and magnify it significantly.