Can a 2nd Visions of Paradise or other irradiation precursor tab affect a map node for a 2nd time?

For example, you have a three tower setup. You complete the 1st tower and use the Visions of Paradise unique tablet and two others. You then complete the 2nd tower adding three more tablets to the mix. Can you then go ahead and complete the nodes irradiated from the 1st tower (removing irradiation), and then complete the 3rd tower adding irradiation back to the nodes that have already been completed once so you can run them again for a second and third time? I suppose the tablet in the third tower doesn't even need to be Visions of Paradise, just a regular precursor tablet adding irradiation.