A crosshair never ruined the illusion in other 3D games I’ve played :\ the laser is just stupid and doesn’t even work well.
For me crosshairs are a bother even in 2d mode :/
I play Doom3 without a crosshair

You can do this in 2 ways that I know of. You can edit the crosshair texture to being nothing, or you can use Sikkmod to remove it.
Of course for the BFG edition I wouldn't even have to do these. Cool, me likes.