Is it possible for your hcg to drop then rise and still have a healthy pregnancy?

Rarely: If labs where levels were run are all the same then it is very unlikely that you would have levels that fell then rose and let to a successful pregnancy. Keep following with your provider to monitor that it is not a tubal pregnancy.

Dubious: There are some specific uncommon situations where you could see this, but it's mostly worrisome. It also depends on "how much" of a drop, and in "what" trimester.