Will iRidium work after updating the firmware on iPhone/iPad/iPod touch?

Do not update the firmware of your device until making sure that iRidium client has been updated accordingly.
If you have problems with the control interface after updating the firmware, do not reinstall iRidium on your iOS device as a first method of fixing, you'll get an HWID changed. Just try to install the newest version of iRIdium for PC, save your project in a new version and upload it again.