What alternator? If its a stock one it probably could if you have a good battery, but that draw will be a lot to be clear, and it may be wise to go to a CS130 or AD130 alternator and upgrade your charge wire
It's about 4 1/2 amps per-bulb. I'm sure a healthy OEM alternator can manage the 18 amps, most of these trucks are running either a 63 or 78 amp alternator.
Kind of a side discussion (which is fine with me), I don't like to see people go to high of amperage alternator. The CS130 I think is rated at 160 amps, and the AD I think is up there too. Both designed for a serpentine belt, the problem comes in when you try to spin that thing with a single V-belt, you get a low battery and that alternator will shread a single V-belt, it's just to much load. IMO, even an alternator around 80 amps is getting close to where dual V-belts would be ideal, certainly anything over 100AMPS really aught to be dual belted. This is one of the reasons we saw some rigs later on run V-belts for the air pump, A/C, Power steering, but a simple manually adjustable serpentine belt, which typically went over the water pump and alternator. It was to handle higher output alternators.
None of this is needed for an extra 9 amps. My square is single headlights, but I've got hella 550 fogs and use them a lot with the low beams. They also draw about 9 amps for the pair. The alternator handles them no problem even at idle with the heater rolling out defrost on high. I'm running a 4 year old ACDelco reman alternator, I believe it's a 78 amp.