I think its unfair to compare a M/T and CVT in a drag as power train of a CVT car has quite more loses compared to an M/T car's power train cuz it has a torque converter instead of clutch. Therefore, a CVT car's power train is bound to deliver lesser power to the wheels as compared to an M/T car.
City 1.5 M/T may give tough time to Civic 1.8 CVT in the first half of the drag however as the cars' speed increase and Civic's torque converter locks, City 1.5 shud be no match for Civic 1.8.
As seeing is believing, watch this famous BBC Top Gear clip of drag race b/w Buggatti Veyron (1000hp, A/T) and McLaren F1(620hp, M/T)
While a Civic 1.8 engine is just 17% powerful than City 1.5, Bugatti is 61% powerful than McLaren. Still, McLaren gives a tough fight.