There may be some thru-hikers around, but it won't be crowded. Not like a summer weekend, certainly. But you will probably see other hikers.
Be prepared for cold temps and bad weather no matter what the forecast says. You can get some weather information here:
Just click the Overmountain Shelter link. Mid-April you can have very nice warm weather, or it can be well below freezing. The last time we hiked that area, in late March, the conditions at Carver Gap were 20 degrees colder than forecast, with very high winds and freezing fog. Good times. (Really.)
If I were going then, I would base my overall packing list on the weather forecast, then bring at least one extra layer of warm clothing top and bottom. (For some reason, I keep re-learning that lesson over and over again....)