Technically speaking, it is plausible. The main hindrance to human-powered flight is that humans aren't biomechanically built for flight; we can produce plenty of power, just not in the right ways to create lift on our own. With a vehicle to convert from leg- and arm-power to airfoil power humans are capable of self-powered flight... though it takes an efficient, lightweight vehicle and a fit human to do it.
As for the specific method in the comic, it's not ideal. Flapping one's arms like bird wings is a difficult way to produce power; a pedal-powered prop or rotor would be easier. Besides the musculoskeletal non-ideal, the harness would restrict the downstroke of the arms, and the rope would continually pull somewhat backwards on the pilot, both of which would siphon power away from the forward (i.e. lift-generating) motion of winged flight.
Without the specific biological knowledge or the proper numbers and equations to crunch currently, I couldn't give a for-sure yes or no, but I'm guessing that since this method is roughly equivalent to trying to lift a 5-10kg block by waving two big paper fans at it, mustmost humans would still have trouble flying with this method, even with the large counterweight.
EDIT: per the discussion pointed out by @Hypnosifl and the realization that blowing fans at something and lifting with wings are actually fairly different mechanics, I revise my answer to still vaguely say that it is plausible, with the added hypothesis that most decently-fit humans could do it.