The Great Smokey Mountains National Park, I believe, holds the dishonorable title of the most polluted national park in the US. It is really crowded. It is really, really bad in the fall, but it’s pretty crowded in the spring, too.
I lived in Knoxville in the late '70s and would make day trips to the park. It is very nice. In my opinion, the spring is better than the fall, but it is nice even in mid-summer and the dead of winter (although some parts get closed in the winter due to weather). This was back when Pigeon Forge was just a wide spot on a 4-lane higway–there was no Dollywood. I’ve been back two or three times since then and didn’t recognize it. The park is still a wonder, though. Particularly if you are into hiking; there are nice trails and very impressive overlooks.
What I lived there, we would avoid going up there on the weekends. You might want to check the local school systems to make sure they are not on spring break the same week you are planning to visit (it should be OK, if I recall correctly, most of the schools take spring break later, in April, to let the weather get a little better).
As the weather goes, the end of March is a period of transition. You could see freezing weather (snow, ice storms, etc…) or it might be very nice (sunny, highs in the 60s to 70s, lows 40s and 50s). Or, you might get both. Chances are, you will get rain (the springs are wet in the mountains).
As far as Gatlinburg or Cherokee, I can’t comment. Living in Knoxville, I always just made day trips (we did go the camping thing a couple of times, but again, try and do it during the week, the weekends are just jam-packed). I’d expect them to pretty much the same, except there is gambling in Cherokee.