No, the brakes cannot be parked using one pedal. The act of pulling up the park brake lever pulls a cable which drives a mechanism that "catches" the pedals to hold them depressed. At the same time a switch at the pedals (adjacent Capt's left pedal) sends a signal to close the park brake valve in the R/H body gear wheel well. If only one pedal is pushed the mechanism cannot catch the pedals and they return to the normal position which also brakes the switch and the park brake valve re-opens. Next time you are in the cockpit just give it a go and you'll see.
From the manual.
The parking brake lever is pulled to set the brakes,
after the brakes have been applied. When the parking brake lever is
pulled, it operates a control linkage, causing two pawls to swing toward the brake pedal bellcrank. The pawls engage the
on the bellcranks and set the parking brake, irrespective of
the hydraulic pressure available.
The parking brake will not set unless both pedals are depressed fully,
from either the pilot’s or co-pilot’s side.
To release the parking brakes, fully depress both brake pedals, then
release them.
.