Is turboshaft fuel efficiency affected by N2 loading?
The free turbine shaft can be called $N_2$, but $N_f$ is more common.
Your fuel control for a turboshaft is not so simple. It requires a Fuel Control Unit and an engine control that needs to know how much torque is being produced at the $N_f$.

A fuel control unit [acts] as an intermediary between the operator's controls and the fuel valve. The operator has a power lever which only controls the engine's potential, not the actual fuel flow. The fuel control unit acts as a computer to determine the amount of fuel flow needed to deliver the power requested by the operator.

and

[A] turboprop or turboshaft engine control system has an additional job to do that is not shared by its turbojet and turbofan counterparts. It must control the speed of the propeller or the free turbine, and it usually governs the pitch angle of the propeller blades. (Source)

If you are not bypassing the FCU and other engine control systems, you do need a varying load to have control over the fuel flow (indirectly).
Running an unloaded turboshaft at high power is very dangerous, as the free turbine will be rotating at RPM's way above its design limits. Unloaded free turbines may also cause an auto shutdown.

By Emoscopes (Own work: drawn using XaraXtreme) [GFDL, CC-BY-SA-3.0 or CC BY 2.5], via Wikimedia Commons

Free turbine engines are now commonly fitted with a device to shut off the fuel supply at the HP cock if torque in the turbine output shaft suddenly falls to zero.
A drawback to the simple free turbine turboprop is its behaviour if the load suddenly falls to zero. In such a case, the unconstrained free turbine overspeeds and will be destroyed by centrifugal forces.

In other words, you do need a load of varying degrees, you cannot test an unloaded fully assembled free turbine engine.
As for efficiency, efficiency is a measure of fuel flow per unit thrust/torque, so a load is needed to get that measurement.