Yes, not days and weeks apart.
"They come on all at once and leave all at once."
Does it mean they all come and go approximately at the same time?
Asymptomatic- shows no symptoms
Symptomatic- shows symptoms
With seroconversion one may have symptoms or may not. If you have symptoms they happen 2-4 weeks post exposure and last 1-2 weeks. They come on all at once and leave all at once. The only way you will ever know that you had ARS during seroconversion is by a positive HIV test. Then you can be diagnosed as having had ARS.