It’s a bit of a tossup on this one. Main characters don’t die, but Tasha JUST had. Picard and Riker probably had plot armor, but the annoyingly combative older Dr Crusher stand in? It seemed plausible enough.
I remember being freaked out by the realization that I was going to grow old. Like really old, someday. That episode stuck with me for that reason.
However, I don’t remember being concerned because Pulaski’s condition was wrapped up in the “solve” of the episode. If she died it would all have been for naught, and there were so many breadcrumbs in the episode pointing to the super-kids as the problem. Most of the episode is just waiting for them to get on with the solution and dragging out the nail biter as long as they can.