Can you have ehlers-danlos syndrome without a parent having it diagnosed?

Yes: Ehlers-danlos syndrome (eds) is a group of inheritable disorders. Some types have autosomal dominant inheritance (everyone with one gene gets the condition) and other types have autosomal recessive inheritance. If both parents have a single recessive gene for the same variety of eds, neither parent will have the condition but their kids have a 25% risk of having eds and 50% risk of being a carrier.