Yes, your Pro upgrade is valid for all of your devices. As long as your device is logged in to your iTunes account, and you have already paid for the upgrade, you will not be charged for an in-App upgrade on that device.
The “Check for Upgrades” button in the App’s upgrade screen will check your upgrade status with your iTunes account and will performa an in-App upgrade on that device without charge. But even if you tapped the in-App ‘upgrade’ button, you would not be charged a second time.
This applies to all your devices: for new devices as well as devices where you have deleted the App, you will only ever have to pay for one upgrade as long as you use the in-App upgrade button and you are logged in to the same iTunes account.
NOTE: the upgrade process will only work if your device is connected to the internet. You can test this by loading any web page in Safari.