Do the joints in adjustable duct elbows need to be taped as well once they're adjusted or are they considered air-tight?
Yes, they do.
No, they are not. Far from it, in fact.
You want to tape every seam in your ductwork, using (as Shirlock pointed out) foil tape. Each exposed seam, whether it's at a connection or part of pre-formed metal like the elbow in question, is a leak point.
Do NOT use Duct or Duck tape as the backing for it degrades over time, faster with heat.
Edit: Even though this is for a bathroom fan, you still want to tape. Why? Because air leakage is moisture leakage, and you do not want to be pumping moisture into your attic. In winter it will lead to frost which will lead to mold.
If you are ducting an exhaust fan from a bathroom or range hood, I would use an adhesive backed foil tape. Don't use regular duct tape on a range vent, clothes dryer or anything with higher heat.