No. If you do not explicitly purchase the product then there will be no charge to you.
This is not one of those cases where you have to explicitly cancel in order to avoid an automatic charge: instead, if you want the product then you have to take action to buy it.
The trial is of limited duration (typically 30 days); the software will refuse to start after the trial expires. (If you are using the software when it expires, then it will give you roughly one hour to save your files before it exits by itself.)
