You absolutely can ignore friction losses, of all sorts. Your measurement may not be of any useful value, but you most certainly can ignore them. Or you can choose to identify the most significant and not ignore them. In either case, the definition of a watt is unchanged.

Of course, this is why I like the elegance of the approach Per is advocating (even if he does wander off into the irrelevant a bit). It seems to be a fairly standard approach among bicyclists, and I'd say for a good reason. The total torque applied to the pedals (i.e. the force applied to each pedal (strain gauge) x the moment of each pedal (a constant)) multiplied by the rpm of those pedals is a direct measure of the wattage produced by the rider, regardless of whether that wattage is spent storing potential energy, producing kinetic energy, or overcoming losses (any losses). It's brilliant in its simplicity.

Joe