No. It does not.

Rubberhose stands apart from all other rigging solutions in that it does not use IK math to create rigs. Because it does not use rotation to create shapes, it is not possible to add FK.

Just in case you are curious about the math

IK is short for Inverse Kinematics. It comes from robotics and to meet this definition, you need a chain of rigid elements that are individually rotated to position the end of the chain at a point in space. You start with the end and work backwards to move each elements rotation to hit that goal.

Backwards movement = Inverse kinematics

FK is short for Forward Kinematics. It means that rather than working with the end of a rigid chain in mind, you rotated each segment, and wherever the end lands is a result of this forward-thinking. In character animation, this is typically used for hand waving.

Rubberhose is different

IK comes from the field of robotics, and (without extra work) has a tendency to look robotic. It is anchored in reality and anything non-realistic needs to be worked into the rig.

Rubberhose was designed backwards, and starts with a smushy/stretchy line that can have realism added to it. Hoses bend and stretch to more naturally fit between the end points of a limb rig. This is a different way to think about rigging and does not create bends with rotation. And that's why FK isn't really a think in Rubberhose.