When a laser is on, it is continuously streaming coherent light. The only way to get "bursts" is to pulse the beam. But, remember the speed of light (c = 299,792,458 m⁄s). A clever answer suggests that humans can generally see a 20-meter long F-14 flying by, which suggests a pulse-on duration of 50 ms, which gives us a pulse length of 14,990 km.
Everybody's different, but I'm going to assume we need the same "off" duration to easily distinguish between pulses. In the electronics world we call that a 50% duty cycle.
OK, laser on = 50 ms, laser off = 50 ms.
Note that this is horribly inefficient and no space captain in his right mind would waste so much off time not firing a laser... unless...
It was honking huge and the optics or emission source couldn't handle a long "on" time and needed the "off" time to cool down. Or maybe we need to charge some batteries. Or maybe we need some taunt time between shots. Let's roll with this.
A 6 kW laser will punch through 1.0" stainless steel, but that's for cutting purposes. The hole is itty-bitty, about 320 μm. But King Goombah's ship is a half-mile long! We need something that will punch a 10-meter hole! So we need 187.5 megawatts. Except, that watts are joules-per-second and our cutter is a continuous-on system. So, to deliver the same whomping impact that one second of cutting would give us we need yet another 20× the power.
3.75 Gigawatts. Take that Doc Brown! But further still, that only cuts through one inch of stainless steel. We need to cut through at least 20 meters of ship to make this worth our while, which brings us up to 147.6 gigawatts. Now we're cooking with gas! And, we're finally at a power level where I could believe the need for a short burst and a long cool-down.
But, for the last part of your question, could you see it?
(A) Your first problem is distance. Remember, that pulse of light is humming along at 300,000 km⁄s. We've already established that the pulse is 14,990 km long. That again for the off-time. Maybe once more so you can enjoy how the pulse looks. Your ships are separated by 44,970 km. That's about 10× the width of the United States or ⅛th the distance from the earth to the moon. You could watch it leave and see it coming, but not see it impact without a telescope.
(B) You need something to burn. Now, there is something there. Hydrogent atoms are about 1-per-cubic centimeter and cosmic dust is 1/1000th that. But we're talking about a 10 meter diameter beam 14,990 km long travelling across 44,970 km of space. It won't be Hollywood spectactular, but it's believable there's something ghosty to see. Our beam encompasses π·r2·h = 1.18×109 cubic meters and will traverse 3 "beam lengths" between the two ships for a total of 3.53×109 cubic meters. That's burning through 35 quadrillion hydrogen atoms and 35 trillion particles of cosmic dust (it sounds like a lot, but it isn't). But I'd like to suspend my disbelief and suggest there'd be something to see, if the lights on your bridge weren't too bright and you weren't fighting for air at the moment.