Speaking from the point of view of London Underground, there are some drivers who drive with the light on some or all of the time, including in darkness or in the tunnels. I'd say roughly 10% or so do.
It is possible to do it, although personally I've never been keen as it does reduce the view, however anything that the driver needs to see should be visible - any trackside signage is either externally illuminated or reflective. However, if the bulb is gone or the sign is dirty this isn't necessarily so, and certainly an unlit signal would be very difficult to spot -- although of course the driver should know the road and not be relying on signage.