transferring information refers to transfer of a signal or energy, without necessarily transferring matter. I.e. it generally refers to the energy disturbance propagating through the matter (like a wave). But it also must be coherent, and retain shape above noise levels so that it can be consistently relied on (i.e. you're respiratory system needs to know the C02 levels consistently against a changing baseline, it can't be confused by noise).
OP:
the currents coming into the axon hillock aren't really impulse shaped from a information processing point of view. The population of voltage-sensitive channels along the membrane generate the impulse, initially in response to the current at the hillock, but like a chain reaction, each sub-population of channels after that is triggered by the population before it, so I don't know how you could choose one or the other, unless you loosened up your definition of impulse. Axons definitely transfer information. Before scientists knew about the cascading current channels, they were surprised at how great of conductors neurons were.