I have two huge laurel hedges and have been pruning, chipping/shredding, mulching and burning for years.
I have never had any bad effects and one big beneficial one and that is from the mulch. I put the chipped and shredded mulch in many beds. It works better for weed and pest control than anything else I have used. Think about it. NOTHING eats a Laurel....well, except for slugs. The beds where I use the Laurel are the healthiest ones I have.
I don't know which genus of Laurel I have but it prevalent in the Pacific Northwest. All over Seattle and Western Washington.
Also, I have many families of Robins who return year after year to nest in these Laurels (I only trim before or after their nesting season) and they seem perfectly fine.