If by "standard" you mean a incandescent tungsten filament bulb, nothing at all.
For a true LED driver power supply, it would be constant current, so the tungsten filament would see 25mA (or whatever the constant current is set for) of DC, and nothing bad would happen (the filament also would not likely illuminate either).
Screwing in an LED bulb with integrated power supply, the external supply will still feed the constant current value, so what happens depends upon the design of the LED bulb's integrated power supply. If 25mA is enough to drive everything, the LED bulb might light up. If 25mA is not enough to drive everything, most likely nothing lights up.