Pulsing that fast is mechanically similar to a continuous laser
Pulsing a laser helps, but if the pulse is too fast, it does not give the plasma time to get out of the way negating the whole point of the pulse. Pulsing a high energy laser 100ish times a second allows time for the plasma to expand and dissipate between shots so that you don't waste a lot of power being absorbed by the opaque plasma cloud. However, because each pulse is only 1mW and DARPA determined several years back that the minimum continuous power output of an anti-personnel laser would be about 1kW, you would need this weapon to pulse about 1 million times per second to reach the minimum power output over time for a militarily useful anti-personnel laser. Pulsing a laser so fast that the plasma can not meaningfully expand between shots like this would result in a similarly wasteful burn pattern as a continuous laser.
But high speed lasers DO make for very good electrolasers
Killing a human with a laser takes a lot of heat and energy. Messing with pulse rates and wave patterns can move this number up or down a little bit, but as it turns out, electrocution is a FAR more efficient way to kill a person requiring only 13.5 watts (0.135A at 100V using an AC current over 1 second is typically fatal). Also electrocution weapons have several distinct advantages over other weapons like thier ability to kill even if you don't hit a vital organ. You can also turn up the voltage and down the amperage to turn the same pulse into a non-lethal stun weapon more similar to a police taser, but with much better range, accuracy, and reusability.
Normally, the obstacle with electrocuting someone is the difficulty of spanning the distance between the weapon and the target because you need some kind of wire to transmit the electrical current to the target; however, one thing that short pulse, powerful lasers are really good at is ionizing a thin, well formed "wire" of air. When it comes to making an ionized plasma filament through the air, the point is to NOT give the plasma time to move out of the way; so, the shorter and more energetic your pulse, the narrower and more energy efficient you can make your plasma filament.
Depending on the range and reliability you are trying to give this weapon, you will need to fire a 7e13W beam for approximately 1e-17 to 4e-15 seconds which is well within your setting's tech limits which means you only need a laser with a total power draw of less than a watt to turn a taser into an electrolaser if you can pulse it fast and hard enough.
So instead of a 1000 watt laser, you could use your miniaturized fast pulse laser technology to make an equally deadly, but much more efficient electrolaser. With modern handheld lasers and tasers already able to exceed power outputs of 10 watts per kilogram, and a standard combat rifle coming in at 3.5kg, it is conceivable using technologies not much more advanced than we have today that you could make a 35 watt electro laser combat rifle capable of delivering a fatal or debilitating shock in just under half a second.
