Am I able to join onto my parents’ plan at anytime? (within the accepted age range, of course).
A dependent can be added to coverage during open enrollment or a special enrollment period, this is the same for a spouse.
Under the Affordable Care Act most plans only allow new enrollment of family members during annual open enrollment periods. Each insurance type has it's own special enrollment period as well (based on qualifying life events) which allow family members to be added to a plan. Some insurance types have short Special Enrollment windows. So as a rule of thumb, you'll want to get added to your family plan ASAP after a qualifying life event.
There are many Special Enrollment opportunities that you can look into.