Close, but not quite. For a given torque (axial) a tube of a certain length will twist a certain amount. If you put the same torque on a longer tube, the twist will be greater. This assumes the twist is measured by how much the two ends are moved out of line with each other.

It's not really work, though you could say energy is stored in the tube when it's twisted, if it's metal. If it's carbon, a significant amount is dissipated as heat. Still tends to resist twisting.

So in a compact, the top tube is part of the system that resists twist due to pedaling forces and due to hand forces as the rider pulls on the handlebar. Those two couples impart a twist that tends to pull the head and seat tubes out of plane, by twisting the downtube and the top tube. Downtube and seat tube stiffness are important. The top tube is shortened in a compact because it approches perpendicular interface with the seat tube. That would represent the shortest top tube. As an additional stiffness benefit, the seat stays get shorter. A compact will be stiffer than a conventional frame, even if they share the same materials and construction, assuming they have stiff seatposts.