If there are mounting holes that would be easy.
Of course, but you have to locate the PCB relative to some reference point on the laser cutter bed, as well as ensuring it is parallel to the axes. Some laser cutters have a (low power) visible laser to assist with alignment, and some have accurate edge rules - but even then it may be a bit fiddly to line something up, especially to a fraction of a mm accuracy as you'd want for PCB edges.
From what I've seen, most people using laser cutters just throw a sheet of material (ply, acrylic, etc) down on the bed and just do a rough alignment before cutting. Even when engraving a logo on an iPhone or MacBook getting within a mm or two is probably good enough even for the "pros".
On a CNC bed it is a piece of cake to clamp down a sheet of sacrificial material, run a short program to drill out the locating pin holes, pop in some pins, place down the PCB panel aligned on the pins, and then run the final program to route out the individual PCBs. Repeat the last few steps as many time as you want.
You can certainly spend time setting up a laser cutter to do something similar in a repeatable manner, but I don't see it being quite as easy. A special purpose laser cutter for this type of task would almost certainly use a camera to align to the fiducials - just need to make sure the smoke from the cutting process doesn't clog up the camera lens.