Line based generic model is usually level based or workplane based and can usually be placed using:
NewFamilyInstance(Curve, FamilySymbol, Level, Structure.StructuralType.NonStructural)
(if it is non-structural)
Of the various non-view based overloads that accept a curve this is the only one that doesn't host the family on the face or a reference to a face.
The curve end points Z can be set to zero because it probably ignores them i.e. unlike structural framing the generic model line based family can't have independent end offsets. You can use a global offset from level with BuiltInParameter.INSTANCE_FREE_HOST_OFFSET_PARAM but the thing is flat in terms of it's insertion.
If you elevated one end it will be by your own parametric means within the family and that will be relative to the level it is hosted on. Realistically you can only achieve this kind of effect by angle from horizontal and changing length of the member to simulate something similar to what you get with structural framing. If you try independent linear dimensions to each end from the level the relationship usually breaks down when those dimensions become equal.
If you need it on a non-level workplane (reference plane etc.) I believe you have to use:
NewFamilyInstance(XYZ, FamilySymbol,Element,StructuralType)
If that works you can then adjust the location line.
