A much better starting point than trying to zap mosquitos in flight. Cover small 2d areas rather than large 3d volumes, and bigger targets. Rats would be easir still, but you would need a serious laser for them, so get it right on the cockroaches first. This could be very useful for guarding entries to commercial kitchens and other food manufacturing facilities.
Do-able. But not recommended. That's like cream left on the counter overnight in a house full of cats.
Cockroaches probably represent less eyeball risk than mosquitoes or flies in general if you limit the trajectory to within a few inches of ground and don't have pets. If you have pets they probably enjoy chasing the roaches anyway.
