Hey. You know I'm always happy to participate.
I don't really know how to answer in very specific terms for Covid-19, but I've read a study suggesting thata long stay in an ICU unit, even upon "full" recovery, may have an impact on longer term health outcomes of the person (increased risk of mortality from other causes, etc) and this risk may be comparatively worse the younger and healthier the person was before critical care.
As for "permanent damage" per se, I presume strong pneumonias, like any other inflammation, can carry a risk of causing fibrosis (scarring) and loss of function of normal pulmonary tissue, but I don't think this is very common.
ICU means a lot of other invasive procedures, and they all carry some risk. I think the most extreme form of critical care is when intubation/ventilation is no longer enough to maintain oxygenation, and your blood needs to be pumped out of the body for oxygenation (a lot more complex than mere dialysis). This is called extracorporeal membrane oxygenation (ECMO) and not all critical care units have the means/personnel to do this.
All this to say that the procedures are so intensive, and life is sustained in such artificial ways, that some (how many?) people with "full recoveries" won't be in perfect condition, i.e., their health isn't reset to a pre-disease level.
Remember I'm not a clinician, so some stuff above may be a bit off the mark, it's just a general impression. Am happy to be corrected by anyone who understands more of this.