Only if they are seen. I can a scenario where your space battleships try to fry each other long distance while enormous numbers of drones try to creep into range, or scout for enemy drones. They are almost certain to get zapped when they attack, so they would definitely be drones, not fighters.
Of course. Hence I wrote
combat drones. Drones would make very useful recon units.
Drone weapons would probably be some variation of nukes or antimatter, in order to get enough punch into a small craft to damage a battleship. You'd want something with range, so bomb pumped lasers, shaped nuclear charges or nuclear propelled kinetic kill projectiles would be likely candidates.
Since my story is going for realism even 1 kiloton nuke detonated on contact with battleship can put it out of commison. Problem is hitting it.
Your scenario could work out though. A battleship docked to a station or lazily sitting in orbit may not be very alert. It could be vulenerable to terrorists launching drones at point blank range or even flying a nuke armed suicide civilian shutte craft into them. Somewhat similar to what happened to the USS Cole.
Even in your scenario, at close range missles might work. Some could carry clouds of reflective glitter to scatter the lasers, allowing warhead armed missles to get through. At long range the lasers would have the time to burn through the glitter, but close up some could get through if you used enough missles. Even if it doesn't, every laser firing at a missle or glitter cloud isn't a laser firing at the ship, so they could be useful even if none hit.
Problem is getting close to a space warship. Acceleration maybe pitiful but a target warship could have an relative velocity of thousands of meters per second. Besides giving them an extra edge against missiles the high relative velocity also makes approaching at point blank range a very daunting task.
Also a missile would be fueled by rocket fuel which could potential explode if heated by a high energy lasers. It wont last nowhere near as long as a chunk of metal with same mass.
One could armour the missile with reflective or someother armour good against lasers. But every kg of armour added makes missile slower giving laser more time to damage it.
As for the glitter thing I have an idea for something similar called fragmentional warheads. Basicaly detonate a large cloud of sharpnel in the orbital path of a station or asteroid. The sharpnel arent guided but neither can a station or asteroid change path to avoid them. The sheer number of sharpnels makes shooting all of them down nearly impossible. And even small number of sharpnel is lethal due to high K.E of objects travelling at typical space velocities.