PWM Modes: Center Aligned and Left Aligned (current consumption)
For a given duty cycle, no the current shouldn't be any different. The timer and CCR is still active for the entire period regardless of if it counts up and resets or counts up then back down (which I believe is the difference between left and center aligned). 

I suppose the capture compare block makes an extra comparison in center aligned if I'm counting right, but that shouldn't increase current in any appreciable amount (if at all)